Entire Functions in Generalized Bernstein Spaces and Their Growth Behavior

被引：0

作者：

Forster, Brigitte ^{[1
]}

Semmler, Gunter ^{[2
]}

机构：

[1] Univ Passau, Fak Informat & Math, Passau, Germany

[2] Tech Univ Bergakad Freiberg, Fak Math & Informat, Freiberg, Germany

来源：

SAMPLING THEORY, A RENAISSANCE: COMPRESSIVE SENSING AND OTHER DEVELOPMENTS | 2015年

关键词：

D O I：

10.1007/978-3-319-19749-4_8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an L-2 (R) function, the famous theorem by Paley and Wiener gives a beautiful relation between extensibility to an entire function of exponential type and the line support of its Fourier transform. However, there is a huge class of entire functions of exponential type which are not square integrable on an axis, but do have integrability properties on certain half lines. In this chapter we investigate such functions, their growth behavior, and their integrability properties in L-P-norms. We show generalizations of a theorem of J. Korevaar and the Paley-Wiener theorem.

引用

页码：307 / 329

页数：23

共 27 条

[1]

Avdonin SA., 1995, Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems

[2]

Babenko K. I., 1965, Amer. Math. Soc. Transl. Ser, V44, P115

[3] INEQUALITIES IN FOURIER-ANALYSIS [J].

BECKNER, W .

ANNALS OF MATHEMATICS, 1975, 102 (01) :159-182

[4]

Boas Jr R.P., 1952, J INDIAN MATH SOC, V16, P127

[5]

Boas Jr R.P., 1939, ANN MATH, V2, P948

[6]

Boas R.P., 1954, Entire functions, V5

[7] Representations for entire functions of exponential type [J].

Boas, RP .

ANNALS OF MATHEMATICS, 1938, 39 :269-286

[8]

Duren P.L., 1970, MONOGRAPHS TXB, V38

[9]

Forster B., 2010, Four short courses on harmonic analysis

[10]

Forster B., 2011, P SAMPTA C SAMPL THE

← 1 2 3 →