Hilbert transforms. Volume 1 / Frederick W. (1947-....) King (2009)

Public ISBD Titre : Hilbert transforms. Volume 1 Type de document : texte imprimé Auteurs : Frederick W. (1947-....) King, Auteur Editeur : Cambridge : Cambridge University Press Année de publication : 2009 Collection : Encyclopedia of mathematics and its applications, ISSN 0953-4806 Importance : XXXVIII-858, XXXVIII-660 p. Présentation : ill. Format : 24 cm. ISBN/ISSN/EAN : 978-0-521-88762-5 Note générale : Bibliogr. p. 745-823. - Index Langues : Anglais (eng) Mots-clés : Hilbert transform Hilbert, Transformation de Index. décimale : 517.3 Calcul intégral. Intégration Résumé : The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications. Note de contenu : Summary : Volume I: 1. Introduction 2. Review of some background mathematics 3. Derivation of the Hilbert transform relations. 4. Some basic properties of the Hilbert transform 5. Relationship between the Hilbert transform and some common transforms 6. The Hilbert transform of periodic functions 7. Inequalities for the Hilbert transform 8. Asymptotic behavior of the Hilbert transform 9. Hilbert transforms of some special functions 10. Hilbert transforms involving distributions 11. The finite Hilbert transform 12. Some singular integral equations 13. Discrete Hilbert transforms 14. Numerical evaluation of Hilbert transforms Hilbert transforms. Volume 1 [texte imprimé] / Frederick W. (1947-....) King, Auteur . - Cambridge : Cambridge University Press, 2009 . - XXXVIII-858, XXXVIII-660 p. : ill. ; 24 cm.. - (Encyclopedia of mathematics and its applications, ISSN 0953-4806) . ISBN : 978-0-521-88762-5 Bibliogr. p. 745-823. - Index Langues : Anglais (eng) Mots-clés : Hilbert transform Hilbert, Transformation de Index. décimale : 517.3 Calcul intégral. Intégration Résumé : The Hilbert transform has many uses, including solving problems in aerodynamics, condensed matter physics, optics, fluids, and engineering. Written in a style that will suit a wide audience (including the physical sciences), this book will become the reference of choice on the topic, whatever the subject background of the reader. It explains all the common Hilbert transforms, mathematical techniques for evaluating them, and has detailed discussions of their application. Especially useful for researchers are the tabulation of analytically evaluated Hilbert transforms, and an atlas that immediately illustrates how the Hilbert transform alters a function. A collection of exercises helps the reader to test their understanding of the material in each chapter. The bibliography is a wide-ranging collection of references both to the classical mathematical papers, and to a diverse array of applications. Note de contenu : Summary : Volume I: 1. Introduction 2. Review of some background mathematics 3. Derivation of the Hilbert transform relations. 4. Some basic properties of the Hilbert transform 5. Relationship between the Hilbert transform and some common transforms 6. The Hilbert transform of periodic functions 7. Inequalities for the Hilbert transform 8. Asymptotic behavior of the Hilbert transform 9. Hilbert transforms of some special functions 10. Hilbert transforms involving distributions 11. The finite Hilbert transform 12. Some singular integral equations 13. Discrete Hilbert transforms 14. Numerical evaluation of Hilbert transforms

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The Cauchy problem / Hector O. (1938-....) Fattorini (2008)

Public ISBD Titre : The Cauchy problem Type de document : texte imprimé Auteurs : Hector O. (1938-....) Fattorini, Auteur Editeur : Cambridge : Cambridge University Press Année de publication : 2008 Collection : Encyclopedia of mathematics and its applications, ISSN 0953-4806 Importance : XXII, 636 p. Présentation : ill. Format : 24 cm ISBN/ISSN/EAN : 978-0-521-09686-7 Note générale : Bibliogr. p. 510-626. - Index Langues : Anglais (eng) Mots-clés : Mathematics (general) Mathematics Differential and Integral Equations Dynamical systems and control theory Mathématiques (général) Mathématiques Équations différentielles et intégrales Systèmes dynamiques et théorie du contrôle Index. décimale : 517.955 Problèmes de Cauchy pour les équations aux dérivées partielles Résumé : This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger, and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students. Note de contenu : Summary : 1. Elements of functional analysis 2. The cauchy problem for some equations of mathematical physics: the abstract cauchy problem 3. Properly posed cauchy problems: general theory 4. Dissipative operators and applications 5. Abstract parabolic equations: applications to second order parabolic equations 6. Perturbation and approximation of abstract differential equations 7. Some improperly posed cauchy problems 8. The abstract cauchy problem for time-dependent equations 9. The cauchy problem in the sense of vector-valued distributions The Cauchy problem [texte imprimé] / Hector O. (1938-....) Fattorini, Auteur . - Cambridge : Cambridge University Press, 2008 . - XXII, 636 p. : ill. ; 24 cm. - (Encyclopedia of mathematics and its applications, ISSN 0953-4806) . ISBN : 978-0-521-09686-7 Bibliogr. p. 510-626. - Index Langues : Anglais (eng) Mots-clés : Mathematics (general) Mathematics Differential and Integral Equations Dynamical systems and control theory Mathématiques (général) Mathématiques Équations différentielles et intégrales Systèmes dynamiques et théorie du contrôle Index. décimale : 517.955 Problèmes de Cauchy pour les équations aux dérivées partielles Résumé : This volume deals with the Cauchy or initial value problem for linear differential equations. It treats in detail some of the applications of linear space methods to partial differential equations, especially the equations of mathematical physics such as the Maxwell, Schrödinger, and Dirac equations. Background material presented in the first chapter makes the book accessible to mathematicians and physicists who are not specialists in this area as well as to graduate students. Note de contenu : Summary : 1. Elements of functional analysis 2. The cauchy problem for some equations of mathematical physics: the abstract cauchy problem 3. Properly posed cauchy problems: general theory 4. Dissipative operators and applications 5. Abstract parabolic equations: applications to second order parabolic equations 6. Perturbation and approximation of abstract differential equations 7. Some improperly posed cauchy problems 8. The abstract cauchy problem for time-dependent equations 9. The cauchy problem in the sense of vector-valued distributions

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