Lapidus, Michel L. (Michel Laurent) 1956
Overview
Works:  44 works in 260 publications in 4 languages and 5,371 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Other, Publishing director 
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(
Book
)
27 editions published between 2000 and 2010 in English and held by 366 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
27 editions published between 2000 and 2010 in English and held by 366 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(
Book
)
34 editions published between 2006 and 2014 in English and held by 362 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 held by 362 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
)
46 editions published in 2004 in English and held by 328 WorldCat member libraries worldwide
46 editions published in 2004 in English and held by 328 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
)
19 editions published between 1999 and 2012 in English and held by 327 WorldCat member libraries worldwide
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the onedimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl2, Lapl4, LapPol3, LapMal2, HeLapl2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl3, LapPol3, LapMal2, HeLapl2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c
19 editions published between 1999 and 2012 in English and held by 327 WorldCat member libraries worldwide
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the onedimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl2, Lapl4, LapPol3, LapMal2, HeLapl2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B.) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl3, LapPol3, LapMal2, HeLapl2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which form a sequence which we assume to be infinite. Important information about the geometry of . c is contained in its geometric zeta function (c(8) = L lj. j=l 2 Introduction We assume throughout that this function has a suitable meromorphic ex tension. The central notion of this book, the complex dimensions of a fractal string . c, is defined as the poles of the meromorphic extension of (c
In search of the Riemann zeros : strings, fractal membranes and noncommutative spacetimes by
Michel L Lapidus(
Book
)
11 editions published in 2008 in English and held by 285 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
11 editions published in 2008 in English and held by 285 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 241 WorldCat member libraries worldwide
14 editions published between 1985 and 1986 in English and held by 241 WorldCat member libraries worldwide
Generalized Minkowski content, spectrum of fractal drums, fractal strings, and the Riemannzetafunction by
Christina Q He(
Book
)
12 editions published in 1997 in English and held by 236 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
12 editions published in 1997 in English and held by 236 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
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
)
16 editions published in 1997 in English and held by 234 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
16 editions published in 1997 in English and held by 234 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
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 213 WorldCat member libraries worldwide
12 editions published between 2001 and 2002 in English and held by 213 WorldCat member libraries worldwide
Progress in inverse spectral geometry by
S. I Andersson(
Book
)
9 editions published in 1997 in English and German and held by 175 WorldCat member libraries worldwide
Most polynomial growth on every halfspace Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t> O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [APS] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* ®E), locally given by 00 K(x, y; t) = L>IAk(~k ® 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::> k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op
9 editions published in 1997 in English and German and held by 175 WorldCat member libraries worldwide
Most polynomial growth on every halfspace Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t> O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [APS] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* ®E), locally given by 00 K(x, y; t) = L>IAk(~k ® 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::> k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op
Fractal geometry and dynamical systems in pure and applied mathematics by Fractal Geometry, Dynamical Systems and Economics PISRS 2011 International Conference on Analysis(
Book
)
5 editions published in 2013 in English and held by 106 WorldCat member libraries worldwide
5 editions published in 2013 in English and held by 106 WorldCat member libraries worldwide
Feynman's operational calculus and beyond : noncommutativity and timeordering by
Gerald W Johnson(
Book
)
10 editions published in 2015 in English and held by 92 WorldCat member libraries worldwide
This title is aimed at providing a coherent, essentially selfcontained, rigorous and comprehensive abstract theory of Feynman's operational calculus for functions of (typically) noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and timeordering (or disentangling) rules in his seminal 1951 paper, as is made clear in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work
10 editions published in 2015 in English and held by 92 WorldCat member libraries worldwide
This title is aimed at providing a coherent, essentially selfcontained, rigorous and comprehensive abstract theory of Feynman's operational calculus for functions of (typically) noncommuting operators. Although it is inspired by Feynman's original heuristic suggestions and timeordering (or disentangling) rules in his seminal 1951 paper, as is made clear in the text, the theory developed in this book also goes well beyond them in a number of directions which were not anticipated in Feynman's work
Fractal geometry and dynamical systems in pure and applied mathematics by Fractal Geometry, Dynamical Systems and Economics PISRS 2011 International Conference on Analysis(
Book
)
5 editions published in 2013 in English and held by 16 WorldCat member libraries worldwide
5 editions published in 2013 in English and held by 16 WorldCat member libraries worldwide
Fractal Geometry and Number Theory Complex Dimensions of Fractal Strings and Zeros of Zeta Functions by
Michel L Lapidus(
)
1 edition published in 2000 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2000 in English and held by 6 WorldCat member libraries worldwide
FORMULES DE TROTTER ET CALCUL OPERATIONNEL DE FEYNMAN by
Michel L Lapidus(
Book
)
2 editions published in 1986 in French and held by 5 WorldCat member libraries worldwide
ON OBTIENT DIVERSES EXTENSIONS DE LA FORMULE DE TROTTER DANS LES CAS LINEAIRE ET NON LINEAIRE. ON UTILISE CERTAINS DES RESULTATS POUR DEFINIR ET ETUDIER UNE MODIFICATION DE L'INTEGRALE DE FEYNMAN SOUS DES HYPOTHESES TRES GENERALES. ON ETUDIE LE COMPORTEMENT ASYMPTOTIQUE DES VALEURS PROPRES DE PROBLEMES AUX LIMITES ELLIPTIQUES AVEC UNE FONCTION POIDS NON DEFINIE. ON POSE LES FONDEMENTS D'UNE INTERPRETATION RIGOUREUSE DU CALCUL OPERATIONNEL DE FEYNMAN POUR DES OPERATEURS QUI NE COMMUTTENT PAS. LA THEORIE PERMET D'ETENDRE ET D'UNIFIER DE NOMBREUX CONCEPTS CLASSIQUES, COMME LES SERIES DE PERTURBATION DE DYSON ET LES DIAGRAMMES DE FEYNMAN ASSOCIES, AINSI QUE LES FORMULES DE TROTTER ET DE FEYNMANKAC
2 editions published in 1986 in French and held by 5 WorldCat member libraries worldwide
ON OBTIENT DIVERSES EXTENSIONS DE LA FORMULE DE TROTTER DANS LES CAS LINEAIRE ET NON LINEAIRE. ON UTILISE CERTAINS DES RESULTATS POUR DEFINIR ET ETUDIER UNE MODIFICATION DE L'INTEGRALE DE FEYNMAN SOUS DES HYPOTHESES TRES GENERALES. ON ETUDIE LE COMPORTEMENT ASYMPTOTIQUE DES VALEURS PROPRES DE PROBLEMES AUX LIMITES ELLIPTIQUES AVEC UNE FONCTION POIDS NON DEFINIE. ON POSE LES FONDEMENTS D'UNE INTERPRETATION RIGOUREUSE DU CALCUL OPERATIONNEL DE FEYNMAN POUR DES OPERATEURS QUI NE COMMUTTENT PAS. LA THEORIE PERMET D'ETENDRE ET D'UNIFIER DE NOMBREUX CONCEPTS CLASSIQUES, COMME LES SERIES DE PERTURBATION DE DYSON ET LES DIAGRAMMES DE FEYNMAN ASSOCIES, AINSI QUE LES FORMULES DE TROTTER ET DE FEYNMANKAC
Le conte du naufragé la quête de l'île merveilleuse by
Michel L Lapidus(
Book
)
2 editions published in 2011 in Egyptian and French and held by 5 WorldCat member libraries worldwide
2 editions published in 2011 in Egyptian and French and held by 5 WorldCat member libraries worldwide
La corde des francsmaçons : noeuds, métamorphoses et lacs d'amour by
Michel L Lapidus(
Book
)
1 edition published in 2006 in French and held by 4 WorldCat member libraries worldwide
1 edition published in 2006 in French and held by 4 WorldCat member libraries worldwide
Domain of dependence by
Michel L Lapidus(
Book
)
1 edition published in 1978 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 1978 in English and held by 4 WorldCat member libraries worldwide
GENERALISATION DE LA FORMULE DE TROTTERLIE. ETUDE DE QUELQUES PROBLEMES LIES A DES GROUPES UNITAIRES by
Michel L Lapidus(
Book
)
1 edition published in 1980 in French and held by 4 WorldCat member libraries worldwide
RAPPELS DE LA THEORIE DES SEMIGROUPES. GENERALISATION DE LA FORMULE DE TROTTER. ETUDE DE QUELQUES PROBLEMES LIES A DES GROUPES UNITAIRES
1 edition published in 1980 in French and held by 4 WorldCat member libraries worldwide
RAPPELS DE LA THEORIE DES SEMIGROUPES. GENERALISATION DE LA FORMULE DE TROTTER. ETUDE DE QUELQUES PROBLEMES LIES A DES GROUPES UNITAIRES
Encyclopaedia of mathematics. Supplement III by
Shreeram Shankar Abhyankar(
)
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
1 edition published in 2002 in English and held by 0 WorldCat member libraries worldwide
This is the third supplementary volume to Kluwer's highly acclaimed twelvevolume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and uptodate Encyclopaedia of Mathematics available
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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 Other Honoree Dedicatee
 Harper, Lawrence H. (Lawrence Hueston) 1938 Other Editor
 Rumbos, Adolfo J. 1962 Other Editor
 Andersson, S. I. (Stig Ingvar) 1945 Other Author Editor
 Nielsen, Lance
 Pearse, Erin P. J. 1975 Editor
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Associated Subjects
Calculus, Operational Commutative algebra Cosmology Differentiable dynamical systems Differential equations, Nonlinear Differential equations, Partial Differential equations, PartialNumerical solutions Ergodic theory Feynman, Richard P.(Richard Phillips), Feynman diagrams Feynman integrals Fractals Functional analysis Functions, Zeta Geometry Geometry, Algebraic Geometry, Riemannian Global differential geometry Harmonic analysis Integrals, Generalized Inverse problems (Differential equations) Mathematics Measure theory Mythology, Egyptian Number theory Operator theory Perturbation (Quantum dynamics) Quantum theory Riemannian manifolds Riemann surfaces Space and time Spectral geometry Spectral theory (Mathematics) String models