A density theorem for lacunary Fourier series

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...

Lacunary Fourier Series on Noncommutative Groups

A New Summability Factor Theorem for Trigonometric Fourier Series

In this paper, a known theorem dealing with | N̄, pn |k summability factors of trigonometric Fourier series has been generalized to | N̄, pn, θn |k summability. Some new results have also been obtained.

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.

Determination of a jump by Fourier and Fourier-Chebyshev series

‎By observing the equivalence of assertions on determining the jump of a‎ ‎function by its differentiated or integrated Fourier series‎, ‎we generalize a‎ ‎previous result of Kvernadze‎, ‎Hagstrom and Shapiro to the whole class of‎ ‎functions of harmonic bounded variation‎. ‎This is achieved without the finiteness assumption on‎ ‎the number of discontinuities‎. ‎Two results on determination of ...