THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS

Authors

  • Agata Bezubik Institute of Mathematics, University of Białystok, Akademicka 2, 15-267 Białystok, Poland
  • Severin Pošta Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, CZ-120 00 Prague http://orcid.org/0000-0001-6291-7410

DOI:

https://doi.org/10.14311/AP.2016.56.0156

Keywords:

trigonometric functions, orthogonal polynomials

Abstract

The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3D lattice is shown in an example.

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Published

2016-06-30

Issue

Vol. 56 No. 3 (2016)

Section

Articles

How to Cite

Bezubik, A., & Pošta, S. (2016). THREE-VARIABLE ALTERNATING TRIGONOMETRIC FUNCTIONS AND CORRESPONDING FOURIER TRANSFORMS. Acta Polytechnica, 56(3), 156-165. https://doi.org/10.14311/AP.2016.56.0156
Received 2016-01-04
Accepted 2016-04-05
Published 2016-06-30