Introduction to Nonharmonic Fourier Series (Pure & Applied Mathematics S.) - Hardcover

An introduction to nonharmonic Fourier series / Robert M. Young

1st edition. Fine copy in the original gilt-blocked cloth. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 257 pp. Contents; 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 Order4 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 Space2 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. Subjects; Fourier series. Pre-Calculus. Infinity. Essays. Mathematics. 1 Kg. Artikel-Nr. 397225

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