arXiv subjects

Aleksander Strasburger

Publications and source records attributed to Aleksander Strasburger.

4 recordsLinked to original sources

arXiv2011

On spherical expansions of smooth $\gr{SU}{n}$-zonal functions on the unit sphere in $\NC^n$

We give a self-contained presentation of a novel approach to a construction of spherical harmonic expansions on the unit sphere in $\NC^n$. We derive a new formula for coefficients of the expansion of a smooth zonal function defined on the unit sphere and apply it in some special cases. The expansion for the Poisson--Szegö kernel for the unit ball in $\NC^n$ obtained by our method coincides with the result obtained originally by G. Folland, and on the other hand disproves results recently presented in a paper of V.A. Menegatto et al..

math.CA↗

arXiv2006

A New Form of the Spherical Expansion of Zonal Functions and Fourier Transforms of SO(d)-Finite Functions

This paper presents recent results obtained by the authors (partly in collaboration with A. Dabrowska) 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.

math-ph↗

arXiv2001

The Weyl Algebra, Spherical Harmonics, and Hahn Polynomials

In this article we apply the duality technique of R. Howe to study the structure of the Weyl algebra. We introduce a one-parameter family of ``ordering maps'', where by an ordering map we understand a vector space isomorphism of the polynomial algebra on $\NR^{2d}$ with the Weyl algebra generated by creation and annihilation operators $a_1, ..., a_d, a_1^+, ..., a_d^+$. Corresponding to these orderings, we construct a one-parameter family of ${\fr sl}_2$ actions on the Weyl algebra, what enables us to define and study certain subspaces of the Weyl algebra -- the space of Weyl spherical harmonics and the space of ``radial polynomials''. For the latter we generalize results of Luck and Biedenharn, Bender et al., and Koornwinder describing the radial elements in terms of continuous Hahn polynomials of the number operator.

math-ph↗

arXiv1998

Class Operators as Intertwining Maps into the Group Algebra

With the aim of completing the previous study by A. Orłowski and the author concerning intertwining maps between induced representations and conjugation representation, termed here weighted class operators, we compute the latter explicitely for the conjugation representation arising from the regular representation in the group algebra of a compact group. To that efect a theorem of Wigner-- Eckart type for weighted class operators obtained from matrix coefficients of irreducible representations of a compact group is proved. Also the previous construction of weighted class operators is reviewed and extended to the case of locally compact groups rather then just compact ones. Submitted for: Proceedings of the II International Workshop "Lie Theory and Its Applications in Physics", August 1997, Clausthal.

math.GR↗