@inproceedings{d4bc0e09ae8348da8af59454c42c6379,
title = "On the equivalence between classical and distributional convergence for Shannon type interpolation series and applications",
abstract = "The distribution theory serves as an important theoretical foundation for some approaches arose from the engineering intuition. Particular examples are approaches based on the delta-”function”. We show that for the Shannon sampling/interpolation series (SSS/SIS) of continuous signals”vanishing” at infinity, the classical notion of convergence given in complex analysis is equivalent with the modern notion given by the distribution theory, in the sense that the SSS converges at a point on the real line, different from the sampling/interpolation point, if and only if it converges distributionally. This result is in spirit of Weyl's Lemma on the Laplace equation. As an extension, we give those results also for the sampling/interpolation series based on the sine-type function.",
keywords = "Band-Limited interpolation, Convergence, Distribution Theory, Divergence, Shannon interpolation series, Shannon sampling series, Sine-type functions",
author = "Ezra Tampubolon and Holger Boche",
note = "Publisher Copyright: {\textcopyright} VDE Verlag GMBH. Berlin. Offenback. All rights reserved.; 11th International ITG Conference on Systems, Communications and Coding, SCC 2017 ; Conference date: 06-02-2017 Through 09-02-2017",
year = "2019",
language = "English",
series = "SCC 2017 - 11th International ITG Conference on Systems, Communications and Coding",
publisher = "VDE VERLAG GMBH",
booktitle = "SCC 2017 - 11th International ITG Conference on Systems, Communications and Coding",
}