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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 033, 8 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.033
(Mi sigma61)
 

This article is cited in 7 scientific papers (total in 7 papers)

A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of $\mathrm{SO}(d)$-Finite Functions

Agata Bezubika, Aleksander Strasburgerb

a Institute of Mathematics, University of Bialystok, Akademicka 2, 15-267 Bialystok, Poland
b Department of Econometrics and Informatics, Warsaw Agricultural University, Nowoursynowska 166, 02-787 Warszawa, Poland
Full-text PDF (202 kB) Citations (7)
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Abstract: This paper presents recent results obtained by the authors (partly in collaboration with A. Da̧browska) concerning expansions of zonal functions on Euclidean spheres into spherical harmonics and some applications of such expansions for problems involving Fourier transforms of functions with rotational symmetry. The method used to derive the expansion formula is based entirely on differential methods and completely avoids the use of various integral identities commonly used in this context. Some new identities for the Fourier transform are derived and as a byproduct seemingly new recurrence relations for the classical Bessel functions are obtained.
Keywords: spherical harmonics; zonal harmonic polynomials; Fourier–Laplace expansions; special orthogonal group; Bessel functions; Fourier transform; Bochner identity.
Received: November 30, 2005; in final form February 17, 2006; Published online March 3, 2006
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Document Type: Article
Language: English
Citation: Agata Bezubik, Aleksander Strasburger, “A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of $\mathrm{SO}(d)$-Finite Functions”, SIGMA, 2 (2006), 033, 8 pp.
Citation in format AMSBIB
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\by Agata Bezubik, Aleksander Strasburger
\paper A~New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of $\mathrm{SO}(d)$-Finite Functions
\jour SIGMA
\yr 2006
\vol 2
\papernumber 033
\totalpages 8
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84889234680}
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  • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Symmetry, Integrability and Geometry: Methods and Applications
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    Abstract page:326
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