A characterization of the closed principal ideals in nonradial Hörmander algebras of holomorphic functions of several variables in terms of the behaviour of the generator is obtained. This result is applied to study the range of convolution operators and ultradifferential operators on spaces of quasianalytic functions of Beurling type. Contrary to what is known to happen in the case of non-quas...

In this paper we study weighted versions of Fourier algebras compact quantum groups. We focus on the spectral aspects these Banach in two different ways. first investigate their Gelfand spectrum, which shows a connection to maximal classical closed subgroup and its complexification. Secondly, specific finite dimensional representations coming from complexification underlying group. demonstrate ...

In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for Lfunctions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem.

Pseudoframes for subspaces have been recently introduced by S. Li and H. Ogawa as a tool to analyze lower dimensional data with arbitrary flexibility of both the analyzing and the dual sequence. In this paper we study Gabor pseudoframes for affine subspaces by focusing on geometrical properties of their associated sets of parameters. We first introduce a new notion of Beurling dimension for dis...

The Beurling-Ahlfors operator reveals a rich structure through its representation as a martingale transform. Using elementary linear algebra and martingale inequalities, we obtain new information on this operator. In particular, Essén-type inequalities are proved for the complex Beurling-Ahlfors operator and its generalization to higher dimensions. Moreover, a new estimate of their norms is obt...

We use Fourier multipliers of the Dirac operator and Cauchy transform to obtain composition theorems and integral representations. In particular we calculate the multiplier of the Π-operator. This operator is the hypercomplex version of the Beurling Ahlfors transform in the plane. The hypercomplex Beuling Ahlfors transform is a direct generalization of the Beurling Ahlfors transform and reduces...

The (un)weighted stability for some matrices on a graph is one of essential hypotheses in time-frequency analysis and applied harmonic analysis. In the first part this paper, we show that localized matrix Beurling algebra, its weighted stabilities different exponents Muckenhoupt weights are equivalent to each other, reciprocal optimal lower bound exponent weight controlled by polynomial another...