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Your search keyword '"Weak convergence"' showing total 2 results
2 results on '"Weak convergence"'

1. On a Dirichlet Series Connected to a Periodic Hurwitz Zeta-Function with Transcendental and Rational Parameter.

Author

Balčiūnas, Aidas, Laurinčikas, Antanas, and Stoncelis, Mindaugas

Subjects
*DIRICHLET series, *ANALYTIC functions, *ZETA functions, *HAAR integral, *ANALYTIC spaces, *TRANSCENDENTAL functions, *FUNCTION spaces
Abstract

In the paper, we construct an absolutely convergent Dirichlet series which in the mean is close to the periodic Hurwitz zeta-function, and has the universality property on the approximation of a wide class of analytic functions. [ABSTRACT FROM AUTHOR]

Published
2023
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2. On Discrete Approximation of Analytic Functions by Shifts of the Lerch Zeta Function.

Author

Rimkevičienė, Audronė and Šiaučiūnas, Darius

Subjects
*ANALYTIC functions, *ZETA functions, *DIRICHLET series, *ANALYTIC spaces, *ARITHMETIC series, *ARBITRARY constants
Abstract

The Lerch zeta function is defined by a Dirichlet series depending on two fixed parameters. In the paper, we consider the approximation of analytic functions by discrete shifts of the Lerch zeta function, and we prove that, for arbitrary parameters and a step of arithmetic progression, there is a closed non-empty subset of the space of analytic functions defined in the critical strip such that its functions can be approximated by discrete shifts of the Lerch zeta function. The set of those shifts is infinite, and it has a positive density. For the proof, the weak convergence of probability measures in the space of analytic functions is applied. [ABSTRACT FROM AUTHOR]

Published
2022
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