Riesz fractional derivatives of a function, Dα xf(x) (also called Riesz potentials), are defined as fractional powers of the Laplacian. Asymptotic expansions for large x are computed for the Riesz fractional derivatives of the Airy function of the first kind, Ai(x), and the Scorer function, Gi(x). Reduction formulas are provided that allow one to express Riesz potentials of products of Airy fun...

Image quality assessment is an important topic in the field of digital image processing. In this study, a full-reference image quality assessment method called Riesz transform and Visual contrast sensitivity-based feature SIMilarity index (RVSIM) is proposed. More precisely, a Log-Gabor filter is first used to decompose reference and distorted images, and Riesz transform is performed on the dec...

The d-dimensional Slepian Gaussian random field {S(t), t ∈ R+} is a mean zero Gaussian process with covariance function ES(s)S(t) = ∏d i=1 max(0, ai − |si − ti|) for ai > 0 and t = (t1, · · · , td) ∈ R+. Small ball probabilities for S(t) are obtained under the L2-norm on [0, 1]d, and under the sup-norm on [0, 1]2 which implies Talagrand’s result for the Brownian sheet. The method of proof for t...

in this paper,~some results on finite dimensional generating spaces of quasi-norm family are established.~the idea of equivalent quasi-norm families is introduced.~riesz lemma is established in this space.~finally,~we re-define b-s fuzzy norm and prove that it induces a generating space of quasi-norm family.

We prove that continuous sentences preserved by the ultramean construction (a generalization of the ultraproduct construction) are exactly those sentences which are approximated by linear sentences. Continuous sentences preserved by linear elementary equivalence are exactly those sentences which are approximated in the Riesz space generated by linear sentences. Also, characterizations for linea...

Abstract We study the minimization of a spectral functional made as sum first eigenvalue Dirichlet Laplacian and relative strength Riesz-type interaction functional. show that when Riesz repulsion is below critical value, existence minimizers occurs. Then we prove, by means an expansion analysis, ball rigid minimizer small enough. Eventually for certain regimes repulsion, regular do not exist.

The aim of this work is to introduce a novel concept, Riesz–Dunkl fractional derivatives, within the context Dunkl-type operators. A particularly noteworthy revelation that when specific parameter κ equals zero, derivative smoothly reduces both well-known Riesz and second-order derivative. Furthermore, we new concept: Sobolev space. This space defined characterized using versatile framework Dun...

In this note we present a review, some considerations and new results about maps with values in distribution space domain σ-finite measure X. Namely, is survey Bessel maps, frames bases (in particular Riesz Gel’fand bases) space. setting, the Riesz-Fischer semi-frames are defined them obtained. Some examples tempered distributions examined.