Bergman, Stefan 18981977
Overview
Works:  85 works in 334 publications in 5 languages and 3,802 library holdings 

Genres:  Mathematical formulae Conference papers and proceedings 
Roles:  Author, Translator, Thesis advisor 
Classifications:  QA360, 517.38 
Publication Timeline
.
Most widely held works by
Stefan Bergman
Integral operators in the theory of linear partial differential equations by
Stefan Bergman(
Book
)
56 editions published between 1961 and 2012 in 4 languages and held by 831 WorldCat member libraries worldwide
The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information
56 editions published between 1961 and 2012 in 4 languages and held by 831 WorldCat member libraries worldwide
The present book deals with the construction of solutions of linear partial differential equations by means of integral operators which transform analytic functions of a complex variable into such solutions. The theory of analytic functions has achieved a high degree of deve lopment and simplicity, and the operator method permits us to exploit this theory in the study of differential equations. Although the study of existence and uniqueness of solutions has been highly developed, much less attention has been paid to the investigation of function theo retical properties and to the explicit construction of regular and singular solutions using a unified general procedure. This book attempts to fill in the gap in this direction. Integral operators of various types have been used for a long time in the mathematical literature. In this connection one needs only to mention Euler and Laplace. The author has not attempted to give a complete account of all known operators, but rather has aimed at developing a unified approach. For this purpose he uses special operators which preserve various function theoretical properties of analytic functions, such as domains of regularity, validity of series development, connection between the coefficients of these developments and location and character of singularities, etc. However, all efforts were made to give a complete bibliography to help the reader to find more detailed information
Kernel functions and elliptic differential equations in mathematical physics by
Stefan Bergman(
Book
)
26 editions published between 1953 and 2013 in 3 languages and held by 798 WorldCat member libraries worldwide
Title Page; Copyright Page; Dedication; Preface; NOTE TO THE READER; Table of Contents; PART A  Boundary Value Problems for Partial Differential Equations of Elliptic Type; CHAPTER I  THEORY OF HEAT CONDUCTION; CHAPTER II  FLUID DYNAMICS; CHAPTER III  ELECTRO AND MAGNETOSTATICS; CHAPTER IV  ELASTICITY; PART B  Kernel Function Methods in the Theory of Boundary Value Problems; CHAPTER I  PROPERTIES OF SOLUTIONS; CHAPTER II  THE KERNEL FUNCTIONS AND THEIR PROPERTIES; CHAPTER III  VARIATIONAL AND COMPARISON THEORY; CHAPTER IV  EXISTENCE THEORY
26 editions published between 1953 and 2013 in 3 languages and held by 798 WorldCat member libraries worldwide
Title Page; Copyright Page; Dedication; Preface; NOTE TO THE READER; Table of Contents; PART A  Boundary Value Problems for Partial Differential Equations of Elliptic Type; CHAPTER I  THEORY OF HEAT CONDUCTION; CHAPTER II  FLUID DYNAMICS; CHAPTER III  ELECTRO AND MAGNETOSTATICS; CHAPTER IV  ELASTICITY; PART B  Kernel Function Methods in the Theory of Boundary Value Problems; CHAPTER I  PROPERTIES OF SOLUTIONS; CHAPTER II  THE KERNEL FUNCTIONS AND THEIR PROPERTIES; CHAPTER III  VARIATIONAL AND COMPARISON THEORY; CHAPTER IV  EXISTENCE THEORY
The kernel function and conformal mapping by
Stefan Bergman(
Book
)
33 editions published between 1950 and 2005 in English and held by 727 WorldCat member libraries worldwide
33 editions published between 1950 and 2005 in English and held by 727 WorldCat member libraries worldwide
Contributions to the theory of partial differential equations by
Lipman Bers(
Book
)
21 editions published between 1954 and 1970 in English and held by 629 WorldCat member libraries worldwide
The book description for the forthcoming "Contributions to the Theory of Partial Differential Equations. (AM33)" is not yet available
21 editions published between 1954 and 1970 in English and held by 629 WorldCat member libraries worldwide
The book description for the forthcoming "Contributions to the Theory of Partial Differential Equations. (AM33)" is not yet available
Sur les fonctions orthogonales de plusieurs variables complexes, avec les applications à la thèorie des fonctions analytiques by
Stefan Bergman(
Book
)
23 editions published between 1941 and 1947 in French and German and held by 252 WorldCat member libraries worldwide
23 editions published between 1941 and 1947 in French and German and held by 252 WorldCat member libraries worldwide
Sur la fonctionnoyau d'un domaine et ses applications dans la théorie des transformations pseudoconformes by
Stefan Bergman(
Book
)
12 editions published in 1948 in French and German and held by 150 WorldCat member libraries worldwide
12 editions published in 1948 in French and German and held by 150 WorldCat member libraries worldwide
Partial differential equations, advanced topics by
Stefan Bergman(
Book
)
15 editions published in 1941 in English and held by 134 WorldCat member libraries worldwide
15 editions published in 1941 in English and held by 134 WorldCat member libraries worldwide
The hodograph method in the theory of compressible fluid. Supplement to Fluid dynamics by Professors von Mises and Friedrichs.
Summer 1941 by
Stefan Bergman(
Book
)
6 editions published between 1942 and 1971 in English and held by 30 WorldCat member libraries worldwide
6 editions published between 1942 and 1971 in English and held by 30 WorldCat member libraries worldwide
LEAA police equipment survey of 1972 by
Stefan Bergman(
)
8 editions published between 1973 and 1977 in English and held by 25 WorldCat member libraries worldwide
8 editions published between 1973 and 1977 in English and held by 25 WorldCat member libraries worldwide
Handguns and handgun ammunition by
Stefan Bergman(
)
3 editions published in 1977 in English and held by 24 WorldCat member libraries worldwide
3 editions published in 1977 in English and held by 24 WorldCat member libraries worldwide
Applications of function theoretical methods in the study of harmonic functions and vectors of three variables by
Stefan Bergman(
Book
)
4 editions published in 1958 in English and held by 23 WorldCat member libraries worldwide
4 editions published in 1958 in English and held by 23 WorldCat member libraries worldwide
Kernel functions and elliptic differential equations in mathematical physics by
Stefan Bergman(
Book
)
5 editions published in 1969 in English and held by 20 WorldCat member libraries worldwide
5 editions published in 1969 in English and held by 20 WorldCat member libraries worldwide
Integral operators in the theory of linear partial differential equations : With 8 fig by
Stefan Bergman(
Book
)
3 editions published between 1961 and 1969 in English and German and held by 10 WorldCat member libraries worldwide
3 editions published between 1961 and 1969 in English and German and held by 10 WorldCat member libraries worldwide
Methods for determination and computation of flow patterns of a compressible fluid by
Stefan Bergman(
Book
)
3 editions published between 1945 and 1946 in English and held by 8 WorldCat member libraries worldwide
A wellknown method of generating stream functions of an incompressible fluid flow is that of taking the imaginary part of an analytic function of a complex variable. In previous publications of the author this method was generalized to the case of subsonic flows of a compressible fluid. Flow patterns, which until the present, have proved impossible to obtain by existing methods, were obtained by this procedure; for example, flows around an obstacle the boundary of which is a closed curve, as well as around nonsymmetric profiles. The procedure can be extended to the case of partially subsonic flows. As this method for obtaining flow patterns of compressible fluid from analytic functions of a compressible fluid requires rather lengthy computations, the present paper is devoted to a detailed discussion of perfoming these computations. The operations are divided into two groups: namely, those which need only be carried out once and for all and then can be tabulated (or put on master cards) and those which have to be repeated in every individual case. A detailed description is given concerning the performance of necessary computations on punch card machines. This description is illustrated by an example
3 editions published between 1945 and 1946 in English and held by 8 WorldCat member libraries worldwide
A wellknown method of generating stream functions of an incompressible fluid flow is that of taking the imaginary part of an analytic function of a complex variable. In previous publications of the author this method was generalized to the case of subsonic flows of a compressible fluid. Flow patterns, which until the present, have proved impossible to obtain by existing methods, were obtained by this procedure; for example, flows around an obstacle the boundary of which is a closed curve, as well as around nonsymmetric profiles. The procedure can be extended to the case of partially subsonic flows. As this method for obtaining flow patterns of compressible fluid from analytic functions of a compressible fluid requires rather lengthy computations, the present paper is devoted to a detailed discussion of perfoming these computations. The operations are divided into two groups: namely, those which need only be carried out once and for all and then can be tabulated (or put on master cards) and those which have to be repeated in every individual case. A detailed description is given concerning the performance of necessary computations on punch card machines. This description is illustrated by an example
Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle by
Stefan Bergman(
Book
)
3 editions published in 1945 in English and held by 7 WorldCat member libraries worldwide
Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects : The expressio for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instancees, it is important to have a single expression representing the whole flow
3 editions published in 1945 in English and held by 7 WorldCat member libraries worldwide
Chaplygin introduced the hodograph method in the theory of compressible fluid flows and developed a method for constructing stream functions of such flows. This method, which has been extensively used in investigation of compressible fluid flows, is limited in certain respects : The expressio for the stream function obtained in this manner can represent only certain types of flow patterns. In general, flow patterns obtained in this way cannot represent the whole flow around an obstacle, but only a part of such a flow, and therefore several expressions are needed in order to obtain the whole flow. On the other hand, in many instancees, it is important to have a single expression representing the whole flow
Fluid dynamics by
Brown University(
Book
)
4 editions published between 1941 and 1942 in English and held by 7 WorldCat member libraries worldwide
4 editions published between 1941 and 1942 in English and held by 7 WorldCat member libraries worldwide
Calculation of particular solutions of linear partial differential equations by the method of integral operators by
Stefan Bergman(
Book
)
4 editions published in 1962 in English and held by 7 WorldCat member libraries worldwide
4 editions published in 1962 in English and held by 7 WorldCat member libraries worldwide
On Twodimensional flows of compressible fluids by
Stefan Bergman(
Book
)
4 editions published between 1944 and 1945 in English and held by 6 WorldCat member libraries worldwide
This report is devoted to the study of twodimensional steady motion of a compressible fluid
4 editions published between 1944 and 1945 in English and held by 6 WorldCat member libraries worldwide
This report is devoted to the study of twodimensional steady motion of a compressible fluid
On twodimensional supersonic flows by
Stefan Bergman(
Book
)
6 editions published in 1949 in English and held by 6 WorldCat member libraries worldwide
In previous reports by the author, the method of operators has been applied to the investigation of twodimensional irrotational flow patterns of an ideal compressible fluid, mostly in the subsonic case. Using a similar approach in the present paper, the author defines two different operators which generate supersonic twodimensional flow patterns from differentiable functions of one real variable (An operator is any rule by means of which one function is converted into another. This concept is discusses in some detail in the body of this paper.) Since operators of the type considered preserve many properties of the functions to which they are applied and since the theory of functions of one real variable is more extensively developed than that of solutions of the compressibility equations, the results obtained can be used as a basis for the investigation of supersonic flow patterns
6 editions published in 1949 in English and held by 6 WorldCat member libraries worldwide
In previous reports by the author, the method of operators has been applied to the investigation of twodimensional irrotational flow patterns of an ideal compressible fluid, mostly in the subsonic case. Using a similar approach in the present paper, the author defines two different operators which generate supersonic twodimensional flow patterns from differentiable functions of one real variable (An operator is any rule by means of which one function is converted into another. This concept is discusses in some detail in the body of this paper.) Since operators of the type considered preserve many properties of the functions to which they are applied and since the theory of functions of one real variable is more extensively developed than that of solutions of the compressibility equations, the results obtained can be used as a basis for the investigation of supersonic flow patterns
Application of the method of the kernel function for solving boundary value problems by
Stefan Bergman(
Book
)
3 editions published in 1960 in English and held by 6 WorldCat member libraries worldwide
3 editions published in 1960 in English and held by 6 WorldCat member libraries worldwide
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Related Identities
 Schiffer, Menahem
 Bers, Lipman Author Editor
 Brown University Graduate School
 Bunten, E. Author
 Klaus, P.
 Herriot, John G. (John George) 19162003
 John, Fritz Author Editor
 Law Enforcement Standards Laboratory Editor
 United States National Bureau of Standards
 National Institute of Law Enforcement and Criminal Justice
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Associated Subjects
Aerodynamics, Supersonic Aerodynamics, SupersonicMathematical models AeronauticsResearch Air flow Ammunition Compressibility Computer science Conformal mapping Differential equations Differential equations, Elliptic Differential equations, Linear Differential equations, Partial Differential equations, PartialNumerical solutions Firearms Fluid dynamics Functional equations Functions Functions, Orthogonal Functions of complex variables Hydrodynamics Integral operators Integrals Kernel functions Mathematical analysis Mathematical physics Mathematics Numerical analysis Pistols PoliceEquipment and supplies Surfaces, Representation of Vector analysis
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Alternative Names
Bergman, S.
Bergman, S. 18981977
Bergman, S. (Stefan), 18981977
Bergman, Stefan
Bergman, Stefan, 1898
Bergmann, S. 18981977
Bergmann, Stefan
Bergmann, Stefan 18981977
Stefan Bergman American mathematician
Stefan Bergman Amerikaans wiskundige (18951977)
Stefan Bergman amerikansk matematikar
Stefan Bergman amerikansk matematiker
Stefan Bergman amerykański matematyk
Stefan Bergman matemático estadounidense
Stefan Bergman matematico statunitense
Stefan Bergman mathématicien américain
Stefan Bergman USamerikanischer Mathematiker
Бергман Стефан
Бергман, Стефан 18951977
Бергман, Стефан Брониславович
ステファン・ベルグマン
Languages