Related papers: Paley-Wiener theorems for slice monogenic function…

In a recent paper, we introduced the concept of generalized partial-slice monogenic functions. The class of these functions includes both the theory of monogenic functions and of slice monogenic functions with values in a Clifford algebra.…

We introduce and study a family of spaces of entire functions in one variable that generalise the classical Paley-Wiener and Bernstein spaces. Namely, we consider entire functions of exponential type $a$ whose restriction to the real line…

Paragrassmann algebras are given a sesquilinear form for which one subalgebra becomes a Hilbert space known as the Segal-Bargmann space. This Hilbert space as well as the ambient space of the paragrassmann algebra itself are shown to have…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We~identify the standard weighted Bergman kernels of spaces of nearly holomorphic functions, in~the sense of Shimura, on~bounded symmetric domains. This also yields a description of the analogous kernels for spaces of…

In this paper we introduce reproducing kernel Hilbert spaces of polyanalytic functions of infinite order. First we study in details the counterpart of the Fock space and related results in this framework. In this case the kernel function is…

We study reproducing kernel Hilbert and Pontryagin spaces of slice hyperholomorphic functions which are analogs of the Hilbert spaces of analytic functions introduced by de Branges and Rovnyak. In the first part of the paper we focus on the…

Very recently, the concept of generalized partial-slice monogenic (or regular) functions has been introduced to unify the theory of monogenic functions and of slice monogenic functions over Clifford algebras. Inspired by the work of A.…

We study the Segal-Bargmann transform on $M(2).$ The range of this transform is characterized as a weighted Bergman space. In a similar fashion Poisson integrals are studied. Using a Gutzmer type formula we characterize the range as a class…

The sharp growth and distortion theorems are established for slice monogenic extensions of univalent functions on the unit disc $\mathbb D\subset \mathbb C$ in the setting of Clifford algebras, based on a new convex combination identity.…

In this paper we present generalisations of Paley-Wiener type theorems to Mellin and (Laplace-)Fourier transforms of rapidly decreasing smooth functions with positive support and log-polyhomogeneous asymptotic expansion at zero. This…

We introduce a family of Cauchy integral formulas for slice and slice regular functions on a real associative *-algebra. For each suitable choice of a real vector subspace of the algebra, a different formula is given, in which the domains…

By correcting, simplifying and extending a result of Morimoto, we prove a Paley-Wiener type theorem for functions of exponential type in a sector. It serves as a sectorial analogue of Polya's theorem on the indicator of entire functions and…

Notions of interpolating variational splines and Paley-Wiener spaces are introduced on a combinatorial graph G. Both of these definitions explore existence of a combinatorial Laplace operator onG. The existence and uniqueness of…

In this paper, we prove that the original Littlewood-Paley $g$-functions can be used to characterize Bergman spaces as well.

We give an elementary proof of the Paley-Wiener theorem for smooth functions for the Dunkl transforms on the real line, establish a similar theorem for L^2-functions and prove identities in the spirit of Bang for L^p-functions. The proofs…

Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener…

In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the…

This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_\theta^{\alpha}$ of order $\alpha$ and skewness…

In this paper we study spaces of holomorphic functions on the Siegel upper half-space $\mathcal U$ and prove Paley-Wiener type theorems for such spaces. The boundary of $\mathcal U$ can be identified with the Heisenberg group $\mathbb H_n$.…