Related papers: High Order Riesz Transforms and Mean Value Formula…

In this paper our aim is to establish the Paley-Wiener Theorems for the Weinstein Transform. Furthermore, some applications are presents, in particular some properties for the generalized translation operator associated with the Weinstein…

In this paper, we will give some results on the support of Dunkl translations on compactly supported functions. Then we will define Dunkl-type $BMO$ space and Riesz transforms for Dunkl transform on $L^\infty$, and prove the boundedness of…

Let $\{\lambda_n\}_n \in \ell^\infty(\mathbb{N})$. In 1960, R. Schatten \cite{SCHATTEN} studied operators of the form $\sum_{n=1}^{\infty}\lambda_n (x_n\otimes \bar{y_n})$, where $\{x_n\}_n$, $\{y_n\}_n$ are orthonormal sequences in a…

Generalized integral formulas involving the generalized modified k-Bessel function $J_{k,\nu }^{c,\gamma ,\lambda }\left( z\right) $ of first kind are expressed in terms generalized $k-$Wright functions. Some interesting special cases of…

Let ${\mathscr{L}}=-\text{div}A\nabla$ be a uniformly elliptic operator on $\mathbb{R}^n$, $n\ge 2$. Let $\Omega$ be an exterior Lipschitz domain, and let ${\mathscr{L}}_D$ and ${\mathscr{L}}_N$ be the operator ${\mathscr{L}}$ on $\Omega$…

Frames and orthonormal bases are naturally linked to bounded operators. To tackle unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also…

We prove sharp power-weighted strong type, weak type and restricted weak type inequalities for the heat and Poisson integral maximal operators, Riesz transform and a Littlewood-Paley type square function, emerging naturally in the harmonic…

In this paper, we introduce a discrete Riesz transforms associated with the non-symmetric trigonometric Heckman-Opdam polynomials of type $A_1$. We prove that they can be extended to a bounded operators on $\ell^p(\mathbb{Z})$,…

Let G be symmetrizable Kac-Moody Lie algebra. In this paper we describe a new class of central operators generalising the Casimir operator. We also prove some properties of these operators and show that these operators move highest weight…

Let $\Delta = \nabla^* \nabla$ be the distinguished Laplacian on a Damek-Ricci space. We prove the $L^{p}$-boundedness of the vector of first-order Riesz transforms $\nabla \Delta^{-1/2}$ in the full range $p\in(1,\infty)$. The most…

In model-based reinforcement learning, the transition matrix and reward vector are often estimated from random samples subject to noise. Even if the estimated model is an unbiased estimate of the true underlying model, the value function…

We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is…

In this paper we consider the generalized little Hankel and Berezin type operators on Besov spaces of holomorphic functions on polydiscs and give results about the boundedness of these operators.

Elementary transformations of equations $A\psi=\lambda\psi$ are considered. The invertibility condition (Theorem 1) is established and similar transformations of Riccati equations in the case of second order differential operator $A$ are…

We study the properties of different type of transforms by means of operational methods and discuss the relevant interplay with many families of special functions. We consider in particular the binomial transform and its generalizations. A…

Transfer operators are conjectural "operators of functoriality," which transfer test measures and (relative) characters from one homogeneous space to another. In previous work, I computed transfer operators associated to spherical varieties…

We develop a functional model for operators arising in the study of boundary-value problems of materials science and mathematical physics. We then provide explicit formulae for the resolvents of the associated extensions of symmetric…

The concept of translation of an operator allows to consider the analogous of shift-invariant subspaces in the class of Hilbert-Schmidt operators. Thus, we extend the concept of average sampling to this new setting, and we obtain the…

Spectral problem for the Dirac operator with regular but not strongly regular boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper is to find conditions under which the…

The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of…