The distance between the general Poisson summation formula and that for bandlimited functions: applications to quadrature formulae

Butzer Paul L.; Schmeisser Gerhard; Stens Rudolf L.

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The distance between the general Poisson summation formula and that for bandlimited functions: applications to quadrature formulae

机译：一般泊松求和公式与带限函数之间的距离：应用于正交公式

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摘要

The general Poisson summation formula of harmonic analysis and analytic number theory can be regarded as a quadrature formula with remainder. The purpose of this investigation is to give estimates for this remainder based on the classical modulus of smoothness and on an appropriate metric for describing the distance of a function from a Bernstein space. Moreover, to be more flexible when measuring the smoothness of a function, we consider Riesz derivatives of fractional order. It will be shown that the use of the above metric in connection with fractional order derivatives leads to estimates for the remainder, which are best possible with respect to the order and the constants. (C) 2017 Elsevier Inc. All rights reserved.

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《Applied and Computational Harmonic Analysis》 |2018年第3期|597-615|共19页
作者
Butzer Paul L.; Schmeisser Gerhard; Stens Rudolf L.;
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作者单位

Rhein Westfal TH Aachen, Lehrstuhl Math A, D-52056 Aachen, Germany;

Univ Erlangen Nurnberg, Dept Math, D-91058 Erlangen, Germany;

Rhein Westfal TH Aachen, Lehrstuhl Math A, D-52056 Aachen, Germany;

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正文语种 eng
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关键词
Harmonic analysis; Non-bandlimited functions; Fractional order Riesz derivatives; Lipschitz spaces; Numerical integration; Formulae with remainders; Derivative-free error estimates; Shift-invariant spaces;

机译：调和分析;无带限函数;分数阶Riesz导数;Lipschitz空间;数值积分;余数公式;无导数误差估计;不变位移空间;

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1. The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley-Wiener theorem for bandlimited signals - their interconnections [J] . P. L. Butzer, P. J. S. G. Ferreira, J. R. Higgins, Applicable Analysis . 2011,第3a4期

机译：频带有限信号的采样定理，泊松求和公式，一般Parseval公式，再生核公式和Paley-Wiener定理-它们的相互联系
2. The Summation Formulae of Euler-Maclaurin, Abel-Plana, Poisson, and their Interconnections with the Approximate Sampling Formula of Signal Analysis [J] . Butzer P.L., Ferreira P.J.S.G., Schmeisser G., Results in mathematics . 2011,第3a4期

机译：Euler-Maclaurin，Abel-Plana，Poisson的求和公式及其与信号分析的近似采样公式的相互关系
3. The Summation Formulae of Euler–Maclaurin, Abel–Plana, Poisson, and their Interconnections with the Approximate Sampling Formula of Signal Analysis [J] . P. L. Butzer, P. J. S. G. Ferreira, G. Schmeisser, Results in Mathematics . 2011,第3a4期

机译：Euler–Maclaurin，Abel–Plana，Poisson的求和公式及其与信号分析的近似采样公式的相互关系
4. Application of atomic functions for construction of new classes of quadrature formulas [C] . Golubin, M.V., Masuk, . 2001

机译：原子函数在构造新的正交公式类中的应用
5. An Extension of the Poisson Summation Formula to a Semi-Direct Product [D] . Lind, Jason 2011

机译：泊松求和公式的扩展到半直接乘积
6. Dualizing the Poisson summation formula. [O] . R J Duffin, H F Weinberger 1991

机译：对偶泊松求和公式。
7. The distance between the general Poisson summation formula and that for bandlimited functions; applications to quadrature formulae [O] . Butzer, Paul L., Schmeisser, Gerhard, Stens, Rudolf L. 2016

机译：一般泊松求和公式与公式之间的距离带限功能;应用于求积分公式
8. Generalized Euler's Formula from Poisson's Summation Formula and Some Applications [R] . Bezerra, V. B., Chaba, A. N. 1984

机译：poisson求和公式的广义Euler公式及其应用

The distance between the general Poisson summation formula and that for bandlimited functions: applications to quadrature formulae

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