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Titre : Functional analysis Type de document : texte imprimé Auteurs : Peter Lax, Auteur Editeur : Hoboken, NJ ; New York ; London ; Sydney ; Chichester : John Wiley Année de publication : 2002, cop. 2022 Autre Editeur : London ; New York ; Sydney : Wiley-Interscience Collection : Pure and applied mathematics, ISSN 0079-8185 Importance : 1 vol. (XIX-580 p.) Présentation : couv. ill. Format : 25 cm ISBN/ISSN/EAN : 978-0-471-55604-6 Note générale : Sommaire (abrégé) : Foreword. Linear Spaces. Linear Maps. The Hahn-Banach Theorem. Applications of the Hahn-Banach Theorem. Normed Linear Spaces. Hilbert Space. Applications of Hilbert Space Results. Duals of Normed Linear Space. Applications of Duality. Weak Convergence. Applications of Weak Convergence. The Weak and Weak* Topologies. Locally Convex Topologies and the Krein-Milman Theorem. Examples of Convex Sets and their Extreme Points. Bounded Linear Maps. Examples of Bounded Linear Maps. Banach Algebras and their Elementary Spectral Theory. Gelfand's Theory of Commutative Banach Algebras. Applications of Gelfand's Theory of Commutative Banach Algebras. Examples of Operators and their Spectra. Compact Maps. Examples of Compact Operators. Positive Compact Operators. Fredholm's Theory of Integral Equations. Invariant Subspaces. Harmonic Analysis on a Halfline. Index Theory. Compact Symmetric Operators in Hilbert Space. Examples of Compact Symmetric Operators.Trace Class and Trace Formula. Spectral Theory of Symmetric, Normal and Unitary Operators. Spectral Theory of Self-Adjoint Operators. Examples of Self-Adjoint Operators. Semigroups of Operators. Groups of Unitary Operators. Examples of Strongly Continuous Semigroups. Scattering Theory. A Theorem of Beurling. Appendix A : The Riesz-Kakutani Representation Theorem. Appendix B : Theory of Distributions. Appendix C : Zorn's Lemma. -- ISBN : 0-471-55604-1 (rel.) .-- PPN 070341362 Langues : Anglais (eng) Tags : Analyse fonctionnelle Analyse fonctionnelle -- Problèmes et exercices Opérateurs, Théorie des Functional analysis Functional analysis -- Problems, exercises, etc. Operator theory Index. décimale : 515.7 Analyse fonctionnelle Résumé : Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. - Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. - Includes an appendix on the Riesz representation theorem (description Wiley)
Note de contenu : Contient des exercices. Bibliogr. en fin de chapitres. Index auteurs. Index sujets Functional analysis [texte imprimé] / Peter Lax, Auteur . - Hoboken, NJ ; New York ; London ; Sydney ; Chichester : John Wiley : London ; New York ; Sydney : Wiley-Interscience, 2002, cop. 2022 . - 1 vol. (XIX-580 p.) : couv. ill. ; 25 cm. - (Pure and applied mathematics, ISSN 0079-8185) .
ISBN : 978-0-471-55604-6
Sommaire (abrégé) : Foreword. Linear Spaces. Linear Maps. The Hahn-Banach Theorem. Applications of the Hahn-Banach Theorem. Normed Linear Spaces. Hilbert Space. Applications of Hilbert Space Results. Duals of Normed Linear Space. Applications of Duality. Weak Convergence. Applications of Weak Convergence. The Weak and Weak* Topologies. Locally Convex Topologies and the Krein-Milman Theorem. Examples of Convex Sets and their Extreme Points. Bounded Linear Maps. Examples of Bounded Linear Maps. Banach Algebras and their Elementary Spectral Theory. Gelfand's Theory of Commutative Banach Algebras. Applications of Gelfand's Theory of Commutative Banach Algebras. Examples of Operators and their Spectra. Compact Maps. Examples of Compact Operators. Positive Compact Operators. Fredholm's Theory of Integral Equations. Invariant Subspaces. Harmonic Analysis on a Halfline. Index Theory. Compact Symmetric Operators in Hilbert Space. Examples of Compact Symmetric Operators.Trace Class and Trace Formula. Spectral Theory of Symmetric, Normal and Unitary Operators. Spectral Theory of Self-Adjoint Operators. Examples of Self-Adjoint Operators. Semigroups of Operators. Groups of Unitary Operators. Examples of Strongly Continuous Semigroups. Scattering Theory. A Theorem of Beurling. Appendix A : The Riesz-Kakutani Representation Theorem. Appendix B : Theory of Distributions. Appendix C : Zorn's Lemma. -- ISBN : 0-471-55604-1 (rel.) .-- PPN 070341362
Langues : Anglais (eng)
Tags : Analyse fonctionnelle Analyse fonctionnelle -- Problèmes et exercices Opérateurs, Théorie des Functional analysis Functional analysis -- Problems, exercises, etc. Operator theory Index. décimale : 515.7 Analyse fonctionnelle Résumé : Includes sections on the spectral resolution and spectral representation of self adjoint operators, invariant subspaces, strongly continuous one-parameter semigroups, the index of operators, the trace formula of Lidskii, the Fredholm determinant, and more. - Assumes prior knowledge of Naive set theory, linear algebra, point set topology, basic complex variable, and real variables. - Includes an appendix on the Riesz representation theorem (description Wiley)
Note de contenu : Contient des exercices. Bibliogr. en fin de chapitres. Index auteurs. Index sujets Réservation
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Code-barres Cote Support Localisation Section Disponibilité Nom du donateur OCA-NI-010288 010288 Ouvrages / Books OCA Bib. Nice Mont-Gros NI-Sous sol-1-Ouvrages Sorti jusqu'au 13/11/2025
Titre : Linear algebra and its applications Type de document : texte imprimé Auteurs : Peter Lax, Auteur Mention d'édition : 2nd edition Editeur : Hoboken, NJ ; New York ; London ; Sydney ; Chichester : John Wiley Année de publication : 2007 Collection : Pure and applied mathematics, ISSN 0079-8185 Importance : 1 vol. (ix-392 p.) Format : 25 cm ISBN/ISSN/EAN : 978-0-471-75156-4 Note générale : "recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematicians bookshelf." (source : American Mathematical Monthly) . -- PPN 12044030X Langues : Anglais (eng) Tags : Algebras, Linear Algèbre linéaire Index. décimale : 512.5 Algèbres linéaire, multilinéaire, multidimensionnelle Résumé : Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student–friendly additions that enhance the book?s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up–to–date coverage of the topic, including : The QR algorithm for finding the eigenvalues of a self–adjoint matrix ; The Householder algorithm for turning self–adjoint matrices into tridiagonal form ; The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space. Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion ; the construction of the Jordan Canonical form of matrices; and Carl Pearcy?s elegant proof of Halmos? conjecture about the numerical range of matrices. Note de contenu : Bibliogr. en fin de chapitre. Index p.373-376 Linear algebra and its applications [texte imprimé] / Peter Lax, Auteur . - 2nd edition . - Hoboken, NJ ; New York ; London ; Sydney ; Chichester : John Wiley, 2007 . - 1 vol. (ix-392 p.) ; 25 cm. - (Pure and applied mathematics, ISSN 0079-8185) .
ISBN : 978-0-471-75156-4
"recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematicians bookshelf." (source : American Mathematical Monthly) . -- PPN 12044030X
Langues : Anglais (eng)
Tags : Algebras, Linear Algèbre linéaire Index. décimale : 512.5 Algèbres linéaire, multilinéaire, multidimensionnelle Résumé : Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student–friendly additions that enhance the book?s accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems. Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces. Further updates and revisions have been included to reflect the most up–to–date coverage of the topic, including : The QR algorithm for finding the eigenvalues of a self–adjoint matrix ; The Householder algorithm for turning self–adjoint matrices into tridiagonal form ; The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space. Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion ; the construction of the Jordan Canonical form of matrices; and Carl Pearcy?s elegant proof of Halmos? conjecture about the numerical range of matrices. Note de contenu : Bibliogr. en fin de chapitre. Index p.373-376 Réservation
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Code-barres Cote Support Localisation Section Disponibilité Nom du donateur OCA-NI-010281 010281 Ouvrages / Books OCA Bib. Nice Mont-Gros NI-Sous sol-1-Ouvrages Sorti jusqu'au 13/11/2025
