Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A theory of Stiefel harmonics


Author: Stephen S. Gelbart
Journal: Trans. Amer. Math. Soc. 192 (1974), 29-50
MSC: Primary 43A85; Secondary 22E45, 33A75
MathSciNet review: 0425519
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: An explicit theory of special functions is developed for the homogeneous space $ SO(n)/SO(n - m)$ generalizing the classical theory of spherical harmonics. This theory is applied to describe the decomposition of the Fourier operator on $ n \times m$ matrix space in terms of operator valued Bessel functions of matrix argument. Underlying these results is a hitherto unnoticed relation between certain irreducible representations of $ SO(n)$ and the polynomial representations of $ GL(m,{\mathbf{C}})$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A85, 22E45, 33A75

Retrieve articles in all journals with MSC: 43A85, 22E45, 33A75


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0425519-8
PII: S 0002-9947(1974)0425519-8
Keywords: Generalized spherical harmonics, Stiefel manifold, representations of $ SO(n)$, holomorphic representations of $ GL(m,{\mathbf{C}})$, Fourier transforms on matrix space, generalized Hankel transforms, Bessel functions of matrix argument
Article copyright: © Copyright 1974 American Mathematical Society