An Introduction to Non-Harmonic Fourier Series, Revised Edition, 93

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