Open AccessMultipliers on Compact Lie Groups
Author(s) -
Norman J. Weiss
Publication year - 1971
Publication title -
proceedings of the national academy of sciences of the united states of america
Language(s) - English
Resource type - Journals
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.68.5.930
Subject(s) - lie group , mathematics , multiplication (music) , infinity , bounded function , operator (biology) , fourier transform , pure mathematics , compact group , group (periodic table) , mathematical analysis , combinatorics , physics , biology , genetics , quantum mechanics , repressor , transcription factor , gene
Sufficient conditions are found for a biinvariant operator on a compact Lie group to be bounded onLp , 1 <p < ∞. The proof uses properties ofg -functions on such a group, and an analog to the familiar relationship between differentiation and multiplication under the Fourier transform.