Fourier Transforms and Approximations Analytical Methods and Special Functions Series
Langue : Anglais
Three classes of Fourier transforms are presented: Fourier (Laplace) transforms on the halfline, Fourier transforms of measures with compact support and Fourier transforms of rapidly decreasing functions (on whole line). The focus is on the behaviour of Fourier transforms in the region of analyticity and the distribution of their zeros. Applications of results are presented: approximation by exponentials on the finite interval; behavior of the nonharmonic Fourier series; Müntz-Szasz's problem of approximation by powers on unit interval; approximation by weighted exponentials on whole line.
1. Auxiliary Informations from the Analysis 2. Distribution of Zeros of Finite Fourier Transforms 3. Estimates of Fourier and Laplace Transforms and Their Applications 4. Stability of Classes of Finite Fourier Transforms 5. Laplace Transforms in the Weighted Spaces Lp and Its Applications 6. Nonharmonic Fourier Series 7. Muntz-Szasz's Problem 8. Fourier Transforms of Rapidly Decreasing Functions 9. Approximate Properties of Systems of Exponents in the Lebesgue's Spaces on All Line
Professional
A M Sedletskii
Date de parution : 09-2000
17.8x25.4 cm
Thème de Fourier Transforms and Approximations :
Mots-clés :
Phragmen Lindelof Theorem; Jensen Formula; Riesz Kernel; Exceptional Function; Entire Function; Eo Rem; Trigonometric Fourier Series; Riesz Basis; Exponential Type; Positive Non-decreasing Function; Laplace Transform; Biorthogonal System; Holder Inequality; Space LP; Prove Statem Ent; Banach Spaces; Conjugate Functionals; Inverse Fourier Transform; Positive Zeros; Blaschke Product; Riemann Lebesgue Theorem; Dx Dy; OO OO; Levinson’s Theorem
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