Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Mean convergence of Fourier series on compact Lie groups


Author: Robert J. Stanton
Journal: Trans. Amer. Math. Soc. 218 (1976), 61-87
MSC: Primary 43A90; Secondary 43A75
DOI: https://doi.org/10.1090/S0002-9947-1976-0420158-9
MathSciNet review: 0420158
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The main result is an $ {L^p}$ mean convergence theorem for the partial sums of the Fourier series of a class function on a compact semi-simple Lie group. A central element in the proof is a Lie group-Lie algebra analog of the theorems in classical Fourier analysis that allow one to pass back and forth between multiplier operators for Fourier series in several variables and multiplier operators for the Fourier transform in Euclidean space. To obtain the $ {L^p}$ mean convergence theorem, the theory of the Hilbert transform with weight function is needed.


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


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 43A90, 43A75

Retrieve articles in all journals with MSC: 43A90, 43A75


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0420158-9
Article copyright: © Copyright 1976 American Mathematical Society