Lapidus, Michel L. (Michel Laurent) 1956
Overview
Works:  45 works in 212 publications in 4 languages and 4,470 library holdings 

Genres:  Conference proceedings 
Roles:  Author, Editor 
Classifications:  QA614.86, 514.742 
Publication Timeline
.
Most widely held works by
Michel L Lapidus
The Feynman integral and Feynman's operational calculus
by
Gerald W Johnson(
)
25 editions published between 2000 and 2010 in English and held by 1,166 WorldCat member libraries worldwide
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results
25 editions published between 2000 and 2010 in English and held by 1,166 WorldCat member libraries worldwide
This book provides the most comprehensive mathematical treatment to date of the Feynman path integral and Feynman's operational calculus. It is accessible to mathematicians, mathematical physicists and theoretical physicists. Including new results and much material previously only available in the research literature, this book discusses both the mathematics and physics background that motivate the study of the Feynman path integral and Feynman's operational calculus, and also provides more detailed proofs of the central results
Fractal geometry, complex dimensions and zeta functions geometry and spectra of fractal strings
by
Michel L Lapidus(
)
34 editions published between 2006 and 2014 in English and and held by 1,035 WorldCat member libraries worldwide
Number theory, spectral geometry, and fractal geometry are interlinked in this indepth study of the vibrations of fractal strings, that is, onedimensional drums with fractal boundary.Key Features of this Second Edition:The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal stringsComplex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectraExplicit formulas are extended to apply to
34 editions published between 2006 and 2014 in English and and held by 1,035 WorldCat member libraries worldwide
Number theory, spectral geometry, and fractal geometry are interlinked in this indepth study of the vibrations of fractal strings, that is, onedimensional drums with fractal boundary.Key Features of this Second Edition:The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal stringsComplex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectraExplicit formulas are extended to apply to
Fractal geometry and applications : a jubilee of Benoît Mandelbrot
(
Book
)
15 editions published in 2004 in English and held by 277 WorldCat member libraries worldwide
15 editions published in 2004 in English and held by 277 WorldCat member libraries worldwide
In search of the Riemann zeros : strings, fractal membranes and noncommutative spacetimes
by
Michel L Lapidus(
Book
)
8 editions published in 2008 in English and held by 268 WorldCat member libraries worldwide
Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possibleor, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line
8 editions published in 2008 in English and held by 268 WorldCat member libraries worldwide
Formulated in 1859, the Riemann Hypothesis is the most celebrated and multifaceted open problem in mathematics. In essence, it states that the primes are distributed as harmoniously as possibleor, equivalently, that the Riemann zeros are located on a single vertical line, called the critical line
Generalized Dyson series, generalized Feynman diagrams, the Feynman integral, and Feynman's operational calculus
by
Gerald W Johnson(
Book
)
14 editions published between 1985 and 1986 in English and held by 261 WorldCat member libraries worldwide
14 editions published between 1985 and 1986 in English and held by 261 WorldCat member libraries worldwide
Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions, with 26 illustrations
by
Michel L Lapidus(
Book
)
3 editions published in 2000 in English and held by 246 WorldCat member libraries worldwide
3 editions published in 2000 in English and held by 246 WorldCat member libraries worldwide
Harmonic analysis and nonlinear differential equations : a volume in honor of Victor L. Shapiro : November 35, 1995, University of California, Riverside
by Conference on Analysis and Partial Differential Equations(
Book
)
14 editions published in 1997 in English and held by 243 WorldCat member libraries worldwide
This volume is a collection of papers dealing with harmonic analysis and nonlinear differential equations and stems from a conference on these two areas and their interface held in November 1995 at the University of California, Riverside, in honor of V.L. Shapiro. There are four papers dealing directly with the use of harmonic analysis techniques to solve challenging problems in nonlinear partial differential equations. There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media. A number of the papers contain open problems in their respective areas
14 editions published in 1997 in English and held by 243 WorldCat member libraries worldwide
This volume is a collection of papers dealing with harmonic analysis and nonlinear differential equations and stems from a conference on these two areas and their interface held in November 1995 at the University of California, Riverside, in honor of V.L. Shapiro. There are four papers dealing directly with the use of harmonic analysis techniques to solve challenging problems in nonlinear partial differential equations. There are also several survey articles on recent developments in multiple trigonometric series, dyadic harmonic analysis, special functions, analysis on fractals, and shock waves, as well as papers with new results in nonlinear differential equations. These survey articles, along with several of the research articles, cover a wide variety of applications such as turbulence, general relativity and black holes, neural networks, and diffusion and wave propagation in porous media. A number of the papers contain open problems in their respective areas
Generalized Minkowski content, spectrum of fractal drums, fractal strings, and the Riemannzetafunction
by
Christina Q He(
Book
)
9 editions published in 1997 in English and held by 242 WorldCat member libraries worldwide
In this work, we will extend most of these results by using, in particular, the notion of generalized Minkowski content which is defined through some suitable 'gauge functions' other than the power functions. (This content is used to measure the irregularity (or 'fractality') of the boundary $\Gamma=\partial\Omega).$ In the situation when the power function is not the natural 'gauge function', this will enable us to obtain more precise estimates, with a broader potential range of applications than in the above papers
9 editions published in 1997 in English and held by 242 WorldCat member libraries worldwide
In this work, we will extend most of these results by using, in particular, the notion of generalized Minkowski content which is defined through some suitable 'gauge functions' other than the power functions. (This content is used to measure the irregularity (or 'fractality') of the boundary $\Gamma=\partial\Omega).$ In the situation when the power function is not the natural 'gauge function', this will enable us to obtain more precise estimates, with a broader potential range of applications than in the above papers
Dynamical, spectral, and arithmetic zeta functions : AMS Special Session on Dynamical, Spectral, and Arithmetic Zeta Functions, January 1516, 1999, San Antonio, Texas
by spectral, and arithmetic Zeta functions AMS Special session on dynamical(
Book
)
12 editions published between 2001 and 2002 in English and held by 226 WorldCat member libraries worldwide
12 editions published between 2001 and 2002 in English and held by 226 WorldCat member libraries worldwide
Progress in inverse spectral geometry
by
S. I Andersson(
Book
)
7 editions published in 1997 in English and German and held by 191 WorldCat member libraries worldwide
7 editions published in 1997 in English and German and held by 191 WorldCat member libraries worldwide
Fractal geometry and number theory : complex dimensions of fractal strings and zeros of zeta functions
by
Michel L Lapidus(
Book
)
14 editions published between 1999 and 2012 in English and held by 97 WorldCat member libraries worldwide
14 editions published between 1999 and 2012 in English and held by 97 WorldCat member libraries worldwide
Fractal geometry and dynamical systems in pure and applied mathematics
by Fractal Geometry, Dynamical Systems and Economics PISRS 2011 International Conference on Analysis(
Book
)
3 editions published in 2013 in English and held by 93 WorldCat member libraries worldwide
3 editions published in 2013 in English and held by 93 WorldCat member libraries worldwide
Fractal geometry and dynamical systems in pure and applied mathematics : PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, November 2011: Messina, Sicily, Italy, AMS Special Session on Fractal Geometry in Pure and Applied Mathematics: in memory of Benoit Mandelbrot, January 2012: Boston, Massachusetts, AMS Special Session on Geometry and Analysis on Fractal Spaces, March 2012: Honolulu, Hawaii
by PISRS (Conference)(
)
3 editions published in 2013 in English and held by 14 WorldCat member libraries worldwide
3 editions published in 2013 in English and held by 14 WorldCat member libraries worldwide
Fractal geometry and applications : a jubilee of Benoît Mandelbrot
(
Book
)
5 editions published in 2004 in English and held by 13 WorldCat member libraries worldwide
5 editions published in 2004 in English and held by 13 WorldCat member libraries worldwide
Fractal geometry and applications: a jubilee of Benoît Mandelbrot
(
Book
)
5 editions published in 2004 in English and held by 12 WorldCat member libraries worldwide
5 editions published in 2004 in English and held by 12 WorldCat member libraries worldwide
Analysis, number theory, and dynamical systems
(
Book
)
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
Multifractals, probability and statistical mechanics, applications
(
Book
)
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 9 WorldCat member libraries worldwide
Fractal geometry and dynamical systems in pure and applied mathematics
by Fractal Geometry, Dynamical Systems and Economics PISRS 2011 International Conference on Analysis(
Book
)
2 editions published in 2013 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2013 in English and held by 8 WorldCat member libraries worldwide
Fractal geometry and applications : a jubilee of Benoît Mandelbrot Geometry : multifractals, probability and statistical mechanics, applications
(
)
1 edition published in 2004 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 6 WorldCat member libraries worldwide
La pierre cubique
by
Michel L Lapidus(
Book
)
3 editions published between 2003 and 2013 in French and held by 5 WorldCat member libraries worldwide
3 editions published between 2003 and 2013 in French and held by 5 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Van Frankenhuysen, Machiel 1967 Editor
 Johnson, Gerald W. 1939 Author
 Mandelbrot, Benoit B. Honoree Dedicatee
 He, Christina Q. 1970 Author
 Shapiro, Victor L. (Victor Lenard) 1924 Honoree Dedicatee
 Harper, Lawrence H. (Lawrence Hueston) 1938 Editor
 Rumbos, Adolfo J. 1962 Editor
 Andersson, S. I. (Stig Ingvar) 1945 Author Editor
 Carfi, David 1971 Editor
 Pearse, Erin P. J. 1975 Editor
Associated Subjects
Calculus, Operational Commutative algebra Differentiable dynamical systems Differential equations, Nonlinear Differential equations, Partial Differential equations, PartialNumerical solutions Ergodic theory Feynman diagrams Feynman integrals Fractals Functional analysis Functions, Zeta Geometry Geometry, Riemannian Harmonic analysis Integrals, Generalized Inverse problems (Differential equations) Mathematics Measure theory Number theory Operator theory Perturbation (Quantum dynamics) Riemannian manifolds Riemann surfaces Space and time Spectral geometry Spectral theory (Mathematics) String models