The sampling theorem, Dirichlet series and Hankel transforms
نویسندگان
چکیده
منابع مشابه
Hankel Determinants of Dirichlet Series
We derive a general expression for the Hankel determinants of a Dirichlet series F (s) and derive the asymptotic behavior for the special case that F (s) is the Riemann zeta function. In this case the Hankel determinant is a discrete analogue of the Selberg integral and can be viewed as a matrix integral with discrete measure. We brie y comment on its relation to Plancherel measures.
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Correspondence: homidan@kfupm. edu.sa Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, P. O. Box 119, Saudi Arabia Abstract Hankel operators and Hankel transforms are required in a number of applications. This article proves a number of theorems that efficiently and accurately approximates a function using Hankel transforms and Hankel sum....
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The paper deals with an extension theorem by Costakis and Vlachou on simultaneous approximation for holomorphic function to the setting of Dirichlet series, which are absolutely convergent in the right half of the complex plane. The derivation operator used in the analytic case is substituted by a weighted backward shift operator in the Dirichlet case. We show the similarities and extensions in...
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The Hankel transform for sequences (defined below) has attracted an increasing amount of attention in recent years. The paper [4] situated its study within the mainstream of research into integer sequences, while papers such as [2] hinted at how the study of certain Hankel transforms can lead to results concerning classical sequences. That paper exploited a link between continued fractions and ...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1992
ISSN: 0377-0427
DOI: 10.1016/0377-0427(92)90001-e