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Beginning functional analysis /
Saxe, Karen.
Beginning functional analysis / Karen Saxe. - xi, 197 pages : illustrations ; 24 cm. - Undergraduate texts in mathematics .
Includes bibliographical references (pages [187]-191) and index.
Introduction: To the Student -- 1. Metric Spaces, Normed Spaces, Inner Product Spaces -- 2. Topology of Metric Spaces -- 3. Measure and Integration -- 4. Fourier Analysis in Hilbert Space -- 5. Introduction to Abstract Linear Operator Theory -- 6. Further Topics -- A. Complex Numbers -- B. Basic Set Theory.
"The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators relating these points as linear transformations on these spaces. The author presents the basics of functional analysis with attention paid to both expository style and technical detail, while getting to interesting results as quickly as possible. The book is accessible to students who have completed first courses in linear algebra and real analysis. Topics are developed in their historical context, with accounts of the past - including biographies - appearing throughout the text. The book offers suggestions and references for further study, and many exercises."--BOOK JACKET.
0387952241 9780387952246
00067916
Functional analysis.
QA320 / .S28 2002
Beginning functional analysis / Karen Saxe. - xi, 197 pages : illustrations ; 24 cm. - Undergraduate texts in mathematics .
Includes bibliographical references (pages [187]-191) and index.
Introduction: To the Student -- 1. Metric Spaces, Normed Spaces, Inner Product Spaces -- 2. Topology of Metric Spaces -- 3. Measure and Integration -- 4. Fourier Analysis in Hilbert Space -- 5. Introduction to Abstract Linear Operator Theory -- 6. Further Topics -- A. Complex Numbers -- B. Basic Set Theory.
"The unifying approach of functional analysis is to view functions as points in some abstract vector space and the differential and integral operators relating these points as linear transformations on these spaces. The author presents the basics of functional analysis with attention paid to both expository style and technical detail, while getting to interesting results as quickly as possible. The book is accessible to students who have completed first courses in linear algebra and real analysis. Topics are developed in their historical context, with accounts of the past - including biographies - appearing throughout the text. The book offers suggestions and references for further study, and many exercises."--BOOK JACKET.
0387952241 9780387952246
00067916
Functional analysis.
QA320 / .S28 2002
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