This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators… Mehr…
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols. New Textbooks>Hardcover>Science>Mathematics>Mathematics, Springer New York Core >2 >T<
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This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on … Mehr…
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols., Springer<
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(*) Derzeit vergriffen bedeutet, dass dieser Titel momentan auf keiner der angeschlossenen Plattform verfügbar ist.
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators… Mehr…
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols. New Textbooks>Hardcover>Science>Mathematics>Mathematics, Springer New York Core >2 >T<
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on … Mehr…
This book presents the basic tools of modern analysis within the context of what might be called the fundamental problem of operator theory: to calculate spectra of specific operators on infinite-dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra; the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C-algebras being three areas of current research activity that require mastery of the material presented here. The notion of spectrum of an operator is based on the more abstract notion of the spectrum of an element of a complex Banach algebra. After working out these fundamentals we turn to more concrete problems of computing spectra of operators of various types. For normal operators, this amounts to a treatment of the spectral theorem. Integral operators require 2 the development of the Riesz theory of compact operators and the ideal L of Hilbert–Schmidt operators. Toeplitz operators require several important tools; in order to calculate the spectra of Toeplitz operators with continuous symbol one needs to know the theory of Fredholm operators and index, the ? structure of the Toeplitz C-algebra and its connection with the topology of curves, and the index theorem for continuous symbols., Springer<
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This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative K-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here.
Detailangaben zum Buch - A Short Course on Spectral Theory William Arveson Author
EAN (ISBN-13): 9780387953007 ISBN (ISBN-10): 0387953000 Gebundene Ausgabe Erscheinungsjahr: 2009 Herausgeber: Springer New York Core >2 >T 152 Seiten Gewicht: 0,367 kg Sprache: eng/Englisch
Buch in der Datenbank seit 2007-05-15T10:04:29+02:00 (Berlin) Detailseite zuletzt geändert am 2024-05-29T00:39:18+02:00 (Berlin) ISBN/EAN: 0387953000
ISBN - alternative Schreibweisen: 0-387-95300-0, 978-0-387-95300-7 Alternative Schreibweisen und verwandte Suchbegriffe: Autor des Buches: arveson, computing, toeplitz, analysis banach spaces Titel des Buches: short course, spectral theory, graduate text mathematics, graduate texts mathematics, the graduate
Daten vom Verlag:
Autor/in: William Arveson Titel: Graduate Texts in Mathematics; A Short Course on Spectral Theory Verlag: Springer; Springer US 139 Seiten Erscheinungsjahr: 2001-11-09 New York; NY; US Sprache: Englisch 153,99 € (DE)
This book presents the basic tools of modern analysis within the context of the fundamental problem of operator theory: to calculate spectra of specific operators on infinite dimensional spaces, especially operators on Hilbert spaces. The tools are diverse, and they provide the basis for more refined methods that allow one to approach problems that go well beyond the computation of spectra: the mathematical foundations of quantum physics, noncommutative k-theory, and the classification of simple C*-algebras being three areas of current research activity which require mastery of the material presented here. The book is based on a fifteen-week course which the author offered to first or second year graduate students with a foundation in measure theory and elementary functional analysis.
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