We establish the inverse Lebedev expansion with respect to parameters and arguments of the modified Bessel functions for an arbitrary function from Hardy’s space H2,A, A> 0. This gives another version of the Fourier-integral-type theorem for the Lebedev transform. The result is generalized for a weighted Hardy space Ĥ2,A ≡ Ĥ2((−A,A);|Γ(1+Rez+iτ)|2dτ), 0 < A < 1, of analytic functions f(z),z = R...

We explain a simple strategy to establish analytic regularity for solutions of second order linear elliptic boundary value problems. The abstract framework presented here helps to understand the proof of analytic regularity in polyhedral domains given in the authors’ paper in Math. Models Methods Appl. Sci. 22 (8) (2012). We illustrate this strategy by considering problems set in smooth domains...

Let dA denote Lebesgue area measure on the unit disk D, normalized so that the measure of D equals 1. For α > −1, we denote by dAα the measure dAα(z) = (α + 1)(1 − |z|2)αdA(z). For 1 ≤ p < +∞, the space L(D, dAα) is a Banach space. The weighted Bergman space Aα is the closed subspace of analytic functions in the Hilbert space L(D, dAα). For each z ∈ D, the application:Lz : A 2 α −→ C is continu...

In this paper, we propose a method for detecting patterns of interest in vector fields. Our method detects patterns in a scaleand rotation-invariant manner. It works by approximating the vector-field data locally using a Laurent polynomial weighted by radial basis functions. The proposed representation is able to model both analytic and non-analytic flow fields. Invariance to scale and rotation...

in the present paper, we introduce some new sequence spaces derived by riesz mean and the notions of almost and strongly almost convergence in a real 2-normed space. some topological properties of these spaces are investigated. further, new concepts of statistical convergence which will be called weighted almost statistical convergence, almost statistical convergence and statistical convergence...

let = be a non-negative matrix. denote by the supremum of those , satisfying the following inequality: where , , and also is increasing, non-negative sequence of real numbers. if we used instead of the purpose of this paper is to establish a hardy type formula for , where is hausdorff matrix and a similar result is also established for where in particular, we apply our results to the cesaro...

We study elliptic and parabolic problems governed by the singular operatorsL=yα1Δx+yα2(Dyy+cyDy−by2),α1,α2∈R in half-space R+N+1={(x,y):x∈RN,y>0}. prove Lp-estimates solvability for associated problems. In language of semigroup theory, we that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space show it has maximal regularity.

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on unit disk, we find their representations as bounded functions certain unbounded self-adjoint operators. We discuss main properties these representation and, especially, describe relations between spectral function and symbols.

Hilbert envelope (HE) is defined as the magnitude of the analytic signal. This work proposes HE based zero frequency filtering (ZFF) approach for the extraction of epochs in high pass filtered speech. Epochs in speech correspond to instants of significant excitation like glottal closure instants. The ZFF method for epoch extraction is based on the signal energy around the impulse at zero freque...