Partial differential equations Vol. IV / Yu. V. Egorov

Public ISBD Titre : Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations Type de document : texte imprimé Auteurs : Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur Editeur : New York : Springer-Verlag Année de publication : 1993 Collection : Encyclopaedia of Mathematical Sciences Importance : 241 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-53363-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. Note de contenu : Contents Chapter 1 Microlocal properties of distributions Chapter 2 Pseudodifferential operators Chapter 3 Fourier integral operators Chapter 4 The propagation of singularities Chapter 5 Solvability of (pseudo) differntial équations Chapter 6 Smoothness of solutions of differential équations Chapter 7 Transformation of boundary-value problems Chapter 8 Hyperfunctions Partial differential equations Vol. IV : microlocal analysis and hyperbolic equations [texte imprimé] / Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur . - New York : Springer-Verlag, 1993 . - 241 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISBN : 978-3-540-53363-4 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : In the first part of this EMS volume Yu.V. Egorov gives an account of microlocal analysis as a tool for investigating partial differential equations. This method has become increasingly important in the theory of Hamiltonian systems. Egorov discusses the evolution of singularities of a partial differential equation and covers topics like integral curves of Hamiltonian systems, pseudodifferential equations and canonical transformations, subelliptic operators and Poisson brackets. The second survey written by V.Ya. Ivrii treats linear hyperbolic equations and systems. The author states necessary and sufficient conditions for C?- and L2 -well-posedness and he studies the analogous problem in the context of Gevrey classes. He also gives the latest results in the theory of mixed problems for hyperbolic operators and a list of unsolved problems. Both parts cover recent research in an important field, which before was scattered in numerous journals. The book will hence be of immense value to graduate students and researchers in partial differential equations and theoretical physics. Note de contenu : Contents Chapter 1 Microlocal properties of distributions Chapter 2 Pseudodifferential operators Chapter 3 Fourier integral operators Chapter 4 The propagation of singularities Chapter 5 Solvability of (pseudo) differntial équations Chapter 6 Smoothness of solutions of differential équations Chapter 7 Transformation of boundary-value problems Chapter 8 Hyperfunctions

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Partial differential equations Vol. VI / Yu. V. Egorov

Public ISBD Titre : Partial differential equations Vol. VI : elliptic and parabolic operators Type de document : texte imprimé Auteurs : Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur Editeur : New York : Springer-Verlag Année de publication : 1994 Collection : Encyclopaedia of Mathematical Sciences Importance : 325 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-54678-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject. Note de contenu : Contents I. Elliptic Operators on Closed Manifolds. II. Degenerate Elliptic Equations and Boundary Problems. III. Parabolic Equations. Author Index. Partial differential equations Vol. VI : elliptic and parabolic operators [texte imprimé] / Yu. V. Egorov, Auteur ; M. A. Shubin, Auteur . - New York : Springer-Verlag, 1994 . - 325 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISSN : 978-3-540-54678-2 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : Authored by well-known researchers, this book presents its material as accessible surveys, giving readers access to comprehensive coverage of results scattered throughout the literature. A unique source of information for graduate students and researchers in mathematics and theoretical physics, and engineers interested in the subject. Note de contenu : Contents I. Elliptic Operators on Closed Manifolds. II. Degenerate Elliptic Equations and Boundary Problems. III. Parabolic Equations. Author Index.

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Probability theory Vol. III / Yu. V. Prokhorov

Public ISBD Titre : Probability theory Vol. III : stochastic calculus Type de document : texte imprimé Auteurs : Yu. V. Prokhorov, Auteur ; A. N. Shiryaev, Auteur ; P. B. Slater, Traducteur Editeur : New York : Springer-Verlag Année de publication : 1998 Collection : Encyclopaedia of Mathematical Sciences Importance : 253 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-54687-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are well-known experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods. Note de contenu : Contents Chapter 1 Introduction to Stochastic Calculus Chapter 2 Stochastic Differential and Evolution Equations I Stochastic Differential Equations (SDEs) II Stochastic Evolution Equations III Stochastic Calculus (Malliavin Calculus). Applications to Stochastic Differential Equations Chapter 3 Stochastic Calculus on Filtered Probability Spaces I Elements of the General Theory of Stochastic Processes II Semimartingales. Stochastic Integrals III Absolute Continuity and Singularity of Probability Distributions Chapter 4 Martingales and Limit Theorems for Stochastic Processes I Theory: Weak Convergence of Probability Measures on Metric Spaces II Applications: The Invariance Principle and Diffusion Approximation Author Index Subject Index Probability theory Vol. III : stochastic calculus [texte imprimé] / Yu. V. Prokhorov, Auteur ; A. N. Shiryaev, Auteur ; P. B. Slater, Traducteur . - New York : Springer-Verlag, 1998 . - 253 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISSN : 978-3-540-54687-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-05 Probabilité et statistique Résumé : This volume of the Encyclopaedia is a survey of stochastic calculus which has become an increasingly important part of probability. The topics covered include Brownian motion, the Ito integral, stochastic differential equations and Malliavin calculus, the general theory of random processes and martingale theory. The five authors are well-known experts in the field. The first chapter of the book is an introduction which treats Brownian motion and describes the developments which lead to the definition of Ito's integral. The book addresses graduate students and researchers in probability theory and mathematical statistics and will also be used by physicists and engineers who need to apply stochastic methods. Note de contenu : Contents Chapter 1 Introduction to Stochastic Calculus Chapter 2 Stochastic Differential and Evolution Equations I Stochastic Differential Equations (SDEs) II Stochastic Evolution Equations III Stochastic Calculus (Malliavin Calculus). Applications to Stochastic Differential Equations Chapter 3 Stochastic Calculus on Filtered Probability Spaces I Elements of the General Theory of Stochastic Processes II Semimartingales. Stochastic Integrals III Absolute Continuity and Singularity of Probability Distributions Chapter 4 Martingales and Limit Theorems for Stochastic Processes I Theory: Weak Convergence of Probability Measures on Metric Spaces II Applications: The Invariance Principle and Diffusion Approximation Author Index Subject Index

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Several complex variables Vol. VII / H. Grauert

Public ISBD Titre : Several complex variables Vol. VII : sheaf-theoretical methods in complex analysis Type de document : texte imprimé Auteurs : H. Grauert, Auteur ; TH. Paternell, Auteur ; R. Remmert, Auteur Editeur : New York : Springer-Verlag Année de publication : 1994 Collection : Encyclopaedia of Mathematical Sciences Importance : 369 p. Présentation : couv. ill. en coul. Format : 24 cm. ISBN/ISSN/EAN : 978-3-540-56259-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : This book offers a systématic introduction to and a comprehensive survey of yhe theory of complex aspaces. the first two chapters cover the founations, then topics as cohomology of complex spaces, analytic and meromorphic decompositions of coplex spaces,the levi problem and vanishing theorems, q-convex and q-convex spaces and bimeromorphic geometry are treated. finally cycle spaces and extension theorems are discussed.this volume is the first survey of the theory of complex spaces and includes various historical remarks. It will be useful to graduate students and reseearchers in complex analysis, algebraic geoltry and differential geometry. also mathematical physicists interested in these fields will find the volume useful. Note de contenu : Contents Introduction Chapter I. Local Theory of Complex Spaces Chapter II. Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces Chapter III. Cohomology Chapter IV. Seminormal Complex Spaces Chapter V. Pseudoconvexity, the Levi Problem and Vanishing Theorems Chapter VI. Theory of q-Convesity and q-Concavity Chapter VII. Modifications Chapter VIII. Cycle Spaces Chapter IX. Extensions of Analytic Objects Author Index Subject Index Several complex variables Vol. VII : sheaf-theoretical methods in complex analysis [texte imprimé] / H. Grauert, Auteur ; TH. Paternell, Auteur ; R. Remmert, Auteur . - New York : Springer-Verlag, 1994 . - 369 p. : couv. ill. en coul. ; 24 cm.. - (Encyclopaedia of Mathematical Sciences) . ISSN : 978-3-540-56259-1 Langues : Anglais (eng) Catégories : MATHEMATIQUES Index. décimale : 04-01 Mathématiques générales Résumé : This book offers a systématic introduction to and a comprehensive survey of yhe theory of complex aspaces. the first two chapters cover the founations, then topics as cohomology of complex spaces, analytic and meromorphic decompositions of coplex spaces,the levi problem and vanishing theorems, q-convex and q-convex spaces and bimeromorphic geometry are treated. finally cycle spaces and extension theorems are discussed.this volume is the first survey of the theory of complex spaces and includes various historical remarks. It will be useful to graduate students and reseearchers in complex analysis, algebraic geoltry and differential geometry. also mathematical physicists interested in these fields will find the volume useful. Note de contenu : Contents Introduction Chapter I. Local Theory of Complex Spaces Chapter II. Differential Calculus, Holomorphic Maps and Linear Structures on Complex Spaces Chapter III. Cohomology Chapter IV. Seminormal Complex Spaces Chapter V. Pseudoconvexity, the Levi Problem and Vanishing Theorems Chapter VI. Theory of q-Convesity and q-Concavity Chapter VII. Modifications Chapter VIII. Cycle Spaces Chapter IX. Extensions of Analytic Objects Author Index Subject Index

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