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Полная версия
ЖУРНАЛЫ // Symmetry, Integrability and Geometry: Methods and Applications // Архив

SIGMA, 2006, том 2, 033, 8 стр. (Mi sigma61)

Эта публикация цитируется в 7 статьях

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

Аннотация: 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.

Ключевые слова: spherical harmonics; zonal harmonic polynomials; Fourier–Laplace expansions; special orthogonal group; Bessel functions; Fourier transform; Bochner identity.

MSC: 33C55; 42B10; 33C80; 44A15; 44A20

Поступила: 30 ноября 2005 г.; в окончательном варианте 17 февраля 2006 г.; опубликована 3 марта 2006 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2006.033



Реферативные базы данных:
ArXiv: math-ph/0603011


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