Lacunary Fourier Series for Compact Quantum Groups

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.

Lacunary Fourier Series on Noncommutative Groups

On the Absolute Convergence of Small Gaps Fourier Series of Functions

Let f be a 2π periodic function in L[0, 2π] and ∑∞ k=−∞ f̂(nk)e inkx be its Fourier series with ‘small’ gaps nk+1 − nk ≥ q ≥ 1. Here we have obtained sufficiency conditions for the absolute convergence of such series if f is of ∧ BV (p) locally. We have also obtained a beautiful interconnection between lacunary and non-lacunary Fourier series.

A note on lacunary series in $mathcal{Q}_K$ spaces

In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.

A Hausdorff–young Inequality for Locally Compact Quantum Groups

Let G be a locally compact abelian group with dual group Ĝ. The Hausdorff–Young theorem states that if f ∈ Lp(G), where 1 ≤ p ≤ 2, then its Fourier transform Fp(f) belongs to Lq(Ĝ) (where 1 p + 1 q = 1) and ||Fp(f)||q ≤ ||f ||p. Kunze and Terp extended this to unimodular and locally compact groups, respectively. We further generalize this result to an arbitrary locally compact quantum group G b...