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Cover: 9780521337175 | An Introduction to Hilbert Space | N. Young | Taschenbuch | Paperback
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An Introduction to Hilbert Space
Taschenbuch von N. Young
Sprache: Englisch

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Beschreibung
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Dr Young has stressed applications of the theory, particularly to the solution of partial differential equations in mathematical physics and to the approximation of functions in complex analysis. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained. It is based on courses given at the University of Glasgow and contains numerous examples and exercises (many with solutions). Thus it will make an excellent first course in Hilbert space theory at either undergraduate or graduate level and will also be of interest to electrical engineers and physicists, particularly those involved in control theory and filter design.
Zusammenfassung
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained.
Inhaltsverzeichnis
Foreword; Introduction; 1. Inner product spaces; 2. Normed spaces; 3. Hilbert and Banach spaces; 4. Orthogonal expansions; 5. Classical Fourier series; 6. Dual spaces; 7. Linear operators; 8. Compact operators; 9. Sturm-Liouville systems; 10. Green's functions; 11. Eigenfunction expansions; 12. Positive operators and contractions; 13. Hardy spaces; 14. Interlude: complex analysis and operators in engineering; 15. Approximation by analytic functions; 16. Approximation by meromorphic functions; Appendix; References; Answers to selected problems; Afterword; Index of notation; Subject index.
Details
Erscheinungsjahr: 2015
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 250
Inhalt: Kartoniert / Broschiert
ISBN-13: 9780521337175
ISBN-10: 0521337178
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Young, N.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 14 mm
Von/Mit: N. Young
Erscheinungsdatum: 25.09.2015
Gewicht: 0,368 kg
preigu-id: 101150670
Zusammenfassung
This textbook is an introduction to the theory of Hilbert space and its applications. The notion of Hilbert space is central in functional analysis and is used in numerous branches of pure and applied mathematics. Some basic familiarity with real analysis, linear algebra and metric spaces is assumed, but otherwise the book is self-contained.
Inhaltsverzeichnis
Foreword; Introduction; 1. Inner product spaces; 2. Normed spaces; 3. Hilbert and Banach spaces; 4. Orthogonal expansions; 5. Classical Fourier series; 6. Dual spaces; 7. Linear operators; 8. Compact operators; 9. Sturm-Liouville systems; 10. Green's functions; 11. Eigenfunction expansions; 12. Positive operators and contractions; 13. Hardy spaces; 14. Interlude: complex analysis and operators in engineering; 15. Approximation by analytic functions; 16. Approximation by meromorphic functions; Appendix; References; Answers to selected problems; Afterword; Index of notation; Subject index.
Details
Erscheinungsjahr: 2015
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Seiten: 250
Inhalt: Kartoniert / Broschiert
ISBN-13: 9780521337175
ISBN-10: 0521337178
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Young, N.
Hersteller: Cambridge University Press
Maße: 229 x 152 x 14 mm
Von/Mit: N. Young
Erscheinungsdatum: 25.09.2015
Gewicht: 0,368 kg
preigu-id: 101150670
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