We study nonuniform sampling in shift-invariant spaces and the construction of Gabor frames with respect to the class of totally positive functions whose Fourier transform factors as ĝ(ξ) = ∏n j=1(1 + 2πiδjξ) −1 e 2 for δ1, . . . , δn ∈ R, c > 0 (in which case g is called totally positive of Gaussian type). In analogy to Beurling’s sampling theorem for the Paley-Wiener space of entire functions...

An irregular wavelet frame has the form W(ψ,Λ) = {aψ( a − b)}(a,b)∈Λ, where ψ ∈ L (R) and Λ is an arbitrary sequence of points in the affine group A = R ×R. Such irregular wavelet frames are poorly understood, yet they arise naturally, e.g., from sampling theory or the inevitability of perturbations. This paper proves that irregular wavelet frames satisfy a Homogeneous Approximation Property, w...

Abstract This paper present an overview of some of the applications of the martingale inequalities of D.L. Burkholder to L-bounds for singular integral operators, concentrating on the Hilbert transform, first and second order Riesz transforms, the Beurling-Ahlfors operator and other multipliers obtained by projections (conditional expectations) of transformations of stochastic integrals. While ...

We study the change of quantization for a class global pseudodifferential operators infinite order in setting ultradifferentiable functions Beurling type. The composition different quantizations as well transpose are also analysed, with applications to Weyl calculus. compare $$\omega $$ -hypoellipticity and -regularity these classes operators.

In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...