Spectral sets of certain functions associated with Dirichlet series

被引：1

作者：

Ishikawa, Hideaki ^{[1
]}

Kamiya, Yuichi ^{[1
]}

机构：

[1] Hachinohe Natl Coll Technol, Aomori 0391192, Japan

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 347卷 / 01期

关键词：

spectral set; zeta function; Dirichlet series; approximation; Euler-Maclaurin summation; support of distribution;

D O I：

10.1016/j.jmaa.2008.05.089

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study spectral sets of functions which are expressed by Dirichlet series on a half-plane. We consider two approaches to study spectral sets of those functions; one is a distribution theoretic approach and the other is an approach to give asymptotic formulas for certain harmonic functions. Our consideration is essentially based on constructing certain expressions and approximations for those functions. (C) 2008 Elsevier Inc. All rights reserved.

引用

页码：204 / 223

页数：20

共 14 条

[1]

Besicovitch AS., 1954, Almost periodic functions

[2]

BEURLING A, 1947, CR HEBD ACAD SCI, P326

[3]

BEURLING A, 1947, ANAL HARMONIQUE, V15, P9

[4]

Bohr H, 1947, ALMOST PERIODIC FUNC

[5]

CARLESON L, 1997, P S PUR MATH, V60, P65

[6]

Davenport H., 2000, MULTIPLICATIVE NUMBE

[7]

EDWARDS HM, 2001, RIEMANNS ZETA FUNCTI

[8] FOUNDATIONS OF THEORY OF DIRICHLET SERIES [J].

HELSON, H .

ACTA MATHEMATICA UPPSALA, 1967, 118 (1-2) :61-&

[9] Spectral sets of certain unbounded functions [J].

Kamiya, Y .

ACTA MATHEMATICA HUNGARICA, 2006, 110 (1-2) :51-65

[10] On spectrums of certain harmonic functions attached to the Riemann zeta-function [J].

Kamiya, Y .

ACTA MATHEMATICA HUNGARICA, 2004, 105 (1-2) :103-114

← 1 2 →