Schechter, Martin
Overview
Works:  47 works in 317 publications in 8 languages and 5,249 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Other 
Classifications:  QA320, 515.724 
Publication Timeline
.
Most widely held works by
Martin Schechter
Principles of functional analysis by
Martin Schechter(
Book
)
55 editions published between 1971 and 2002 in 3 languages and held by 1,038 WorldCat member libraries worldwide
Functional analysis plays a crucial role in the applied sciences as well as in mathematics. In keeping with this fact the author has made this advanced textbook accessible to a wide range of students including advanced undergraduates
55 editions published between 1971 and 2002 in 3 languages and held by 1,038 WorldCat member libraries worldwide
Functional analysis plays a crucial role in the applied sciences as well as in mathematics. In keeping with this fact the author has made this advanced textbook accessible to a wide range of students including advanced undergraduates
Modern methods in partial differential equations : an introduction by
Martin Schechter(
Book
)
71 editions published between 1961 and 2014 in 4 languages and held by 704 WorldCat member libraries worldwide
"When first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Requiring only some familiarity with advanced calculus and rudimentary complex function theory, it covered discoveries of the previous three decades, a particularly fruitful era. Now it remains a permanent, muchcited contribution to the everexpanding literature on partial differential equations"
71 editions published between 1961 and 2014 in 4 languages and held by 704 WorldCat member libraries worldwide
"When first published in 1977, this volume made recent accomplishments in its field available to advanced undergraduates and beginning graduate students of mathematics. Requiring only some familiarity with advanced calculus and rudimentary complex function theory, it covered discoveries of the previous three decades, a particularly fruitful era. Now it remains a permanent, muchcited contribution to the everexpanding literature on partial differential equations"
Spectra of partial differential operators by
Martin Schechter(
Book
)
24 editions published between 1971 and 1986 in 3 languages and held by 517 WorldCat member libraries worldwide
;Contents: Functional analysis; Function spaces; Partial differential operators; General (L sup P) theory; Relative compactness; Elliptic operators; Operators bounded from below; Selfadjoint extensions; Second order operators; Applications
24 editions published between 1971 and 1986 in 3 languages and held by 517 WorldCat member libraries worldwide
;Contents: Functional analysis; Function spaces; Partial differential operators; General (L sup P) theory; Relative compactness; Elliptic operators; Operators bounded from below; Selfadjoint extensions; Second order operators; Applications
Operator methods in quantum mechanics by
Martin Schechter(
Book
)
24 editions published between 1981 and 2014 in English and Undetermined and held by 467 WorldCat member libraries worldwide
This advanced undergraduate and graduatelevel text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. Lebesgue integration theory and complex variables are sometimes involved, but most of the book can be understood without them. Exercises at the end of each chapter provide helpful reinforcement
24 editions published between 1981 and 2014 in English and Undetermined and held by 467 WorldCat member libraries worldwide
This advanced undergraduate and graduatelevel text introduces the power of operator theory as a tool in the study of quantum mechanics, assuming only a working knowledge of advanced calculus and no background in physics. The author presents a few simple postulates describing quantum theory, gradually introducing the mathematical techniques that help answer questions important to the physical theory; in this way, readers see clearly the purpose of the method and understand the accomplishment. The entire book is devoted to the study of a single particle moving along a straight line. By posing questions about the particle, the text gradually leads readers into the development of mathematical techniques that provide the answers. Lebesgue integration theory and complex variables are sometimes involved, but most of the book can be understood without them. Exercises at the end of each chapter provide helpful reinforcement
An introduction to nonlinear analysis by
Martin Schechter(
Book
)
20 editions published between 2004 and 2012 in English and held by 295 WorldCat member libraries worldwide
Schechter's book deploys nonlinear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving nonlinear problems is developed whilst demonstrating their application
20 editions published between 2004 and 2012 in English and held by 295 WorldCat member libraries worldwide
Schechter's book deploys nonlinear methods using the least background material possible and the simplest linear techniques. An understanding of the tools for solving nonlinear problems is developed whilst demonstrating their application
Critical point theory and its applications by
Wenming Zou(
Book
)
19 editions published in 2006 in English and held by 210 WorldCat member libraries worldwide
"Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications. The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrodinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition."Publisher's website
19 editions published in 2006 in English and held by 210 WorldCat member libraries worldwide
"Since the birth of the calculus of variations, researchers have discovered that variational methods, when they apply, can obtain better results than most other methods. Moreover, they apply in a very large number of situations. It was realized many years ago that the solutions of a great number of problems are in effect critical points of functionals. Critical Point Theory and Its Applications presents some of the latest research in the area of critical point theory. Researchers have obtained many new results recently using this approach, and in most cases comparable results have not been obtained with other methods. This book describes the methods and presents the newest applications. The topics covered in the book include extrema, even valued functionals, weak and double linking, sign changing solutions, Morse inequalities, and cohomology groups. The applications described include Hamiltonian systems, Schrodinger equations and systems, jumping nonlinearities, elliptic equations and systems, superlinear problems and beam equations. Many minimax theorems are established without the use of the (PS) compactness condition."Publisher's website
Spectra of partial differential operators by
Martin Schechter(
Book
)
10 editions published in 1986 in English and held by 198 WorldCat member libraries worldwide
10 editions published in 1986 in English and held by 198 WorldCat member libraries worldwide
Linking methods in critical point theory by
Martin Schechter(
Book
)
15 editions published between 1998 and 2012 in English and held by 195 WorldCat member libraries worldwide
As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the TransCanada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on
15 editions published between 1998 and 2012 in English and held by 195 WorldCat member libraries worldwide
As is well known, The Great Divide (a.k.a. The Continental Divide) is formed by the Rocky Mountains stretching from north to south across North America. It creates a virtual "stone wall" so high that wind, rain, snow, etc. cannot cross it. This keeps the weather distinct on both sides. Since railroad trains cannot climb steep grades and tunnels through these mountains are almost formidable, the Canadian Pacific Railroad searched for a mountain pass providing the lowest grade for its tracks. Employees discovered a suitable mountain pass, called the Kicking Horse Pass, el. 5404 ft., near Banff, Alberta. (One can speculate as to the reason for the name.) This pass is also used by the TransCanada Highway. At the highest point of the pass the railroad tracks are horizontal with mountains rising on both sides. A mountain stream divides into two branches, one flowing into the Atlantic Ocean and the other into the Pacific. One can literally stand (as the author did) with one foot in the Atlantic Ocean and the other in the Pacific. The author has observed many mountain passes in the Rocky Mountains and Alps. What connections do mountain passes have with nonlinear partial dif ferential equations? To find out, read on
Topics in critical point theory by
Kanishka Perera(
Book
)
11 editions published between 2011 and 2013 in English and held by 182 WorldCat member libraries worldwide
"This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, pLaplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research"
11 editions published between 2011 and 2013 in English and held by 182 WorldCat member libraries worldwide
"This book introduces the reader to powerful methods of critical point theory and details successful contemporary approaches to many problems, some of which had proved resistant to attack by older methods. Topics covered include Morse theory, critical groups, the minimax principle, various notions of linking, jumping nonlinearities and the Fučík spectrum in an abstract setting, sandwich pairs and the cohomological index. Applications to semilinear elliptic boundary value problems, pLaplacian problems and anisotropic systems are given. Written for graduate students and research scientists, the book includes numerous examples and presents more recent developments in the subject to bring the reader up to date with the latest research"
Minimax systems and critical point theory by
Martin Schechter(
Book
)
19 editions published in 2009 in English and held by 80 WorldCat member libraries worldwide
Many problems in science and engineering involve the solution of differential equations or systems. One of most successful methods of solving nonlinear equations is the determination of critical points of corresponding functionals. The study of critical points has grown rapidly in recent years and has led to new applications in other scientific disciplines. This monograph continues this theme and studies new results discovered since the author's preceding book entitled Linking Methods in Critical Point Theory. Written in a clear, sequential exposition, topics include semilinear problems, Fucik spectrum, multidimensional nonlinear wave equations, elliptic systems, and sandwich pairs, among others. With numerous examples and applications, this book explains the fundamental importance of minimax systems and describes how linking methods fit into the framework. Minimax Systems and Critical Point Theory is accessible to graduate students with some background in functional analysis, and the new material makes this book a useful reference for researchers and mathematicians. Review of the author's previous Birkhäuser work, Linking Methods in Critical Point Theory: The applications of the abstract theory are to the existence of (nontrivial) weak solutions of semilinear elliptic boundary value problems for partial differential equations, written in the form Au = f(x, u). ... The author essentially shows how his methods can be applied whenever the nonlinearity has sublinear growth, and the associated functional may increase at a certain rate in every direction of the underlying space. This provides an elementary approach to such problems. ... A clear overview of the contents of the book is presented in the first chapter, while bibliographical comments and variant results are described in the last one.MathSciNet
19 editions published in 2009 in English and held by 80 WorldCat member libraries worldwide
Many problems in science and engineering involve the solution of differential equations or systems. One of most successful methods of solving nonlinear equations is the determination of critical points of corresponding functionals. The study of critical points has grown rapidly in recent years and has led to new applications in other scientific disciplines. This monograph continues this theme and studies new results discovered since the author's preceding book entitled Linking Methods in Critical Point Theory. Written in a clear, sequential exposition, topics include semilinear problems, Fucik spectrum, multidimensional nonlinear wave equations, elliptic systems, and sandwich pairs, among others. With numerous examples and applications, this book explains the fundamental importance of minimax systems and describes how linking methods fit into the framework. Minimax Systems and Critical Point Theory is accessible to graduate students with some background in functional analysis, and the new material makes this book a useful reference for researchers and mathematicians. Review of the author's previous Birkhäuser work, Linking Methods in Critical Point Theory: The applications of the abstract theory are to the existence of (nontrivial) weak solutions of semilinear elliptic boundary value problems for partial differential equations, written in the form Au = f(x, u). ... The author essentially shows how his methods can be applied whenever the nonlinearity has sublinear growth, and the associated functional may increase at a certain rate in every direction of the underlying space. This provides an elementary approach to such problems. ... A clear overview of the contents of the book is presented in the first chapter, while bibliographical comments and variant results are described in the last one.MathSciNet
Uravnenija s častnymi proizvodnymi by
Lawrence C Evans(
Book
)
5 editions published in 1966 in Russian and held by 12 WorldCat member libraries worldwide
5 editions published in 1966 in Russian and held by 12 WorldCat member libraries worldwide
Lectures in applied mathematics : proceedings of the summer seminar, Boulder, Colorado, 1957 by Summer seminar on applied mathematics(
Book
)
4 editions published between 1959 and 1960 in English and held by 7 WorldCat member libraries worldwide
4 editions published between 1959 and 1960 in English and held by 7 WorldCat member libraries worldwide
Pian wei fen fang cheng di xian dai fang fa by
Martin Schechter(
Book
)
1 edition published in 1983 in Chinese and held by 3 WorldCat member libraries worldwide
1 edition published in 1983 in Chinese and held by 3 WorldCat member libraries worldwide
Curs de algebră şi programare liniară : pentru uzul studenţilor by
Martin Schechter(
Book
)
3 editions published between 1979 and 1983 in Romanian and Undetermined and held by 3 WorldCat member libraries worldwide
3 editions published between 1979 and 1983 in Romanian and Undetermined and held by 3 WorldCat member libraries worldwide
Radiculosaccography with watersoluble contrast media by
P Capesius(
Book
)
2 editions published between 1978 and 2014 in English and held by 3 WorldCat member libraries worldwide
2 editions published between 1978 and 2014 in English and held by 3 WorldCat member libraries worldwide
Lectures in applied mathematics. proceedings of the summer seminar, Boulder, Colorado (June 23 to July 19,) 1957 : (sponsored
by the American Mathematical Society) : Probability and related topics in physical sciences(
Book
)
1 edition published in 1959 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1959 in English and held by 2 WorldCat member libraries worldwide
Die Giganten des Fuenfjahrplanes by
Michail E Šechter(
Book
)
1 edition published in 1931 in German and held by 2 WorldCat member libraries worldwide
1 edition published in 1931 in German and held by 2 WorldCat member libraries worldwide
Prevalence of antibodies to Hepatitis C virus in populations at low and high risk for sexually transmited diseases in Rio
de Janeiro by M. Edelenyi Pinto(
)
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
In order to investigate the sexual transmission of the Hepatitis C Virus (HCV), the prevalence of specific antibodies in populations at high and low risk for sexually transmitted diseases (STDs) was evaluated. The population at low risk for STDs was composed of persons who voluntarity donated blood at the Hospital Universitario Clementino Fraga Filho (HUCFF) between July and November, 1990 (n = 2494). The population at high risk for STDs was drawn from an ongoing study on the natural history of Human Immunodeficiency Virus (HIV) infection (n = 210, 187 with sexual risk factors for HIV infection). All samples were screened using a first generation ELISA. Repeat reactive samples were then tested in a second generation RIBA. For all ELISA positive samples, two sex and agematched ELISA negative controls were selected. Data pertaining to the presence of antibodies to the Hepatitis B core antigen (antiHBC antibodies) and to Treponema pallidum were abstracted from the medical records. The prevalence of RIBA 2 confirmed HCV infection among the blood donors was 2.08%, which is well above the reported prevalence in similar populations from developed western countries. Among the HIV infected homosexuals, the encountered prevalence was 7.96% (p <0.0005). For the whole group with sexually acquired HIV infection, the prevalence was 8.02% (p <0.000005). AntiHBc antibodies were more frequently present in antiHCV RIBA2 confirmed positive blood donors than in controls (p <0.001). 33.3% of the HCVpositive blood donors and 11.04% controls were found to be antiHBc positive (p <0.0005). As for the FTAABs, 17.6% HCVpositive donors and 4,9% controls were positive (p <0.01). 5.9% samples from blood donors were both antiHBc and FTAABS positive, whereas none of the controls reacted in both tests (p <0.05). The association between HCV, Hepatitis B infection and syphilis in individuals at low risk for parenterally transmitted diseases suggests that sexual transmission contributes to the maintenance of the endemicity of HCV in the local population
1 edition published in 1993 in English and held by 1 WorldCat member library worldwide
In order to investigate the sexual transmission of the Hepatitis C Virus (HCV), the prevalence of specific antibodies in populations at high and low risk for sexually transmitted diseases (STDs) was evaluated. The population at low risk for STDs was composed of persons who voluntarity donated blood at the Hospital Universitario Clementino Fraga Filho (HUCFF) between July and November, 1990 (n = 2494). The population at high risk for STDs was drawn from an ongoing study on the natural history of Human Immunodeficiency Virus (HIV) infection (n = 210, 187 with sexual risk factors for HIV infection). All samples were screened using a first generation ELISA. Repeat reactive samples were then tested in a second generation RIBA. For all ELISA positive samples, two sex and agematched ELISA negative controls were selected. Data pertaining to the presence of antibodies to the Hepatitis B core antigen (antiHBC antibodies) and to Treponema pallidum were abstracted from the medical records. The prevalence of RIBA 2 confirmed HCV infection among the blood donors was 2.08%, which is well above the reported prevalence in similar populations from developed western countries. Among the HIV infected homosexuals, the encountered prevalence was 7.96% (p <0.0005). For the whole group with sexually acquired HIV infection, the prevalence was 8.02% (p <0.000005). AntiHBc antibodies were more frequently present in antiHCV RIBA2 confirmed positive blood donors than in controls (p <0.001). 33.3% of the HCVpositive blood donors and 11.04% controls were found to be antiHBc positive (p <0.0005). As for the FTAABs, 17.6% HCVpositive donors and 4,9% controls were positive (p <0.01). 5.9% samples from blood donors were both antiHBc and FTAABS positive, whereas none of the controls reacted in both tests (p <0.05). The association between HCV, Hepatitis B infection and syphilis in individuals at low risk for parenterally transmitted diseases suggests that sexual transmission contributes to the maintenance of the endemicity of HCV in the local population
Die Grossbauten des Kommunismus und das Verkehrswesens(
Book
)
1 edition published in 1952 in German and held by 1 WorldCat member library worldwide
1 edition published in 1952 in German and held by 1 WorldCat member library worldwide
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Boundary value problems Chebyshev approximation Critical point theory (Mathematical analysis) Differential equations Differential equations, Nonlinear Differential equations, Partial Differential operators Fixed point theory Functional analysis Global analysis (Mathematics) Lumbosacral regionRadiography Mathematical physics Mathematics Maxima and minima Mechanics Nonlinear boundary value problems Nonlinear functional analysis Nonlinear theories Numerical analysis Operator theory Partial differential operators Quantum theory Radiographic contrast media Relativity (Physics) Spectral theory (Mathematics) Spinal nerve rootsRadiography
Alternative Names
Martin Schechter American mathematician
Martin Schechter Amerikaans wiskundige
Martin Schechter USamerikanischer Mathematiker
Schechter, M.
Schechter, Martin
Šechter, M. 1930
Šehter, M.
Шехтер, М..
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