An Introduction to Nonharmonic Fourier Series
Published on 9. January 1981
245 pages
978-0-08-087409-8 (ISBN)
Description
An Introduction to Nonharmonic Fourier Series
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Robert M. Young
Introduction to Nonharmonic Fourier Series
Book
11/1980
Academic Press
€75.52
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Content
- Front Cover
- An Introduction to Nonharmonic Fourier Series
- Copyright Page
- CONTENTS
- Preface
- Chapter 1. Bases in Banach Spaces
- 1 Schauder Bases
- 2 Schauder's Basis for C[a,b]
- 3 Orthonormal Bases in Hilbert Space
- 4 The Reproducing Kernel
- 5 Complete Sequences
- 6 The Coefficient Functionals
- 7 Duality
- 8 Reisz Bases
- 9 The Stability of Bases in Banach Spaces
- 10 The Stability of Orthonormal Bases in Hilbert Space
- Chapter 2. Entire Functions of Exponential Type
- Part One. The Classical Factorization Theorems
- 1 Weierstrass's Factorization Theorem
- 2 Jensen's Formula
- 3 Functions of Finite Order
- 4 Estimates for Canonical Products
- 5 Hadamard's Factorization Theorem
- Part Two. Restrictions along a Line
- 1 The "Phragmén-Lindelöf" Method
- 2 Carleman's Formula
- 3 Integrability on a Line
- 4 The Paley-Wiener Theorem
- 5 The Paley-Wiener Space
- Chapter 3. The Completeness of Sets of Complex Exponentials
- 1 The Trigonometric System
- 2 Exponentials Close to the Trigonometric System
- 3 A Counterexample
- 4 Some Intrinsic Properties of Sets of Complex Exponentials
- 5 Stability
- 6 Density and the Completeness Radius
- Chapter 4. Interpolation and Bases in Hilbert Space
- 1 Moment Sequences in Hilbert Space
- 2 Bessel Sequences and Riesz-Fischer Sequences
- 3 Applications to Systems of Complex Exponentials
- 4 The Moment Space and Its Relation to Equivalent Sequences
- 5 Interpolation in the Paley-Wiener Space: Functions of Sine Type
- 6 Interpolation in the Paley-Wiener Space: Stability
- 7 The Theory of Frames
- 8 The Stability of Nonharmonic Fourier Series
- 9 Pointwise Convergence
- Notes and Comments
- References
- List of Special Symbols
- Author Index
- Subject Index
