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# An Introduction to Non Harmonic Fourier Series Revised

**Robert Young**

ISBN **0127729550**

Pages **252**

Description

An Introduction to Non-Harmonic Fourier Series, Revised Edition is an update of a widely known and highly respected classic textbook.

Throughout the book, material has also been added on recent developments, including stability theory, the frame radius, and applications to signal analysis and the control of partial differential equations.

Contents

Bases in Banach Spaces - Schauder Bases; Schauder's Basis for C[a,b]; Orthonormal Bases in Hilbert Space; The Reproducing Kernel; Complete Sequences; The Coefficient Functionals; Duality; Riesz Bases; The Stability of Bases in Banach Spaces; The Stability of Orthonormal Bases in Hilbert Space Entire Functions of Exponential Type The Classical Factorization Theorems - Weierstrass's Factorization Theorem; Jensen's Formula; Functions of Finite Order; Estimates for Canonical Products; Hadamard's Factorization Theorem Restrictions Along a Line - The Phragmen-Lindelof' Method; Carleman's Formula; Integrability on a line; The Paley-Wiener Theorem; The Paley-Wiener Space The Completeness of Sets of Complex Exponentials - The Trigonometric System; Exponentials Close to the Trigonometric System; A Counterexample; Some Intrinsic Properties of Sets of Complex Exponentials Stability; Density and the Completeness Radius Interpolation and Bases in Hilbert Space - Moment Sequences in Hilbert Space; Bessel Sequences and Riesz-Fischer Sequences; Applications to Systems of Complex Exponentials; The Moment Space and Its Relation to Equivalent Sequences; Interpolation in the Paley-Wiener Space: Functions of Sine Type; Interpolation in the Paley-Wiener Space: Stability; The Theory of Frames; The Stability of Nonharmonic Fourier Series; Pointwise Convergence; Notes and Comments; References; List of Special Symbols Index '