A Family of Generalized Riesz Products

GENERALIZED RIESZ PRODUCTS ON THE BOHR COMPACTIFICATION OF Rp ̊q

We study a class of generalized Riesz products connected to the spectral type of some class of rank one flows on R. Applying a Central Limit Theorem of Kac, we exhibit a large class of singular generalized Riesz products on the Bohr compactification of R. Moreover, we discuss the problem of the flat polynomials in this setting. Dedicated to Professors Jean-Paul Thouvenot and Bernard Host. AMS S...

A characterization of L-dual frames and L-dual Riesz bases

This paper is an investigation of $L$-dual frames with respect to a function-valued inner product, the so called $L$-bracket product on $L^{2}(G)$, where G is a locally compact abelian group with a uniform lattice $L$. We show that several well known theorems for dual frames and dual Riesz bases in a Hilbert space remain valid for $L$-dual frames and $L$-dual Riesz bases in $L^{2}(G)$.

Covering the Large Spectrum and Generalized Riesz Products

Chang’s Lemma is a widely employed result in additive combinatorics. It gives optimal bounds on the dimension of the large spectrum of probability distributions on nite abelian groups. In this note, we show how Chang’s Lemma and a powerful variant due to Bloom both follow easily from an approximation theorem for probability measures in terms of generalized Riesz products. The latter result invo...

G-Frames, g-orthonormal bases and g-Riesz bases

G-Frames in Hilbert spaces are a redundant set of operators which yield a representation for each vector in the space. In this paper we investigate the connection between g-frames, g-orthonormal bases and g-Riesz bases. We show that a family of bounded operators is a g-Bessel sequences if and only if the Gram matrix associated to its denes a bounded operator.

Generalized Frames in Hilbert Spaces