Fourier series on compact Lie groups

Lacunary Fourier Series for Compact Quantum Groups

This paper is devoted to the study of Sidon sets, Λ(p)-sets and some related notions for compact quantum groups. We establish several different characterizations of Sidon sets, and in particular prove that any Sidon set in a discrete group is a strong Sidon set in the sense of Picardello. We give several relations between Sidon sets, Λ(p)-sets and lacunarities for LFourier multipliers, generali...

The Existence of Nonabsolutely Convergent Fourier Series on Compact Groups

1. J. W. S. Cassels, An introduction to diophantine approximation, Cambridge University Press, 1959, Chapter IV, §5. 2. J. F. Koksma, Diophantische Approximationen, Ergebnisse der Mathematik, vol. IV, Berlin, Springer, 1937, Chapter VIII, §3. 3. G. M. Petersen, Almost convergence and uniformly distributed sequences, Quart. J. Math. vol. 7 (1956) pp. 188-191. 4. H. Weyl, Uber die Gleichverteilun...

Lacunary Fourier series and a qualitative uncertainty principle for compact Lie groups

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L1(G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

Probability on Compact Lie Groups

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.