Related papers: Fourier Representations in Bergman Spaces
Polymer representations of the Weyl algebra of linear systems provide the simplest analogues of the representation used in loop quantum gravity. The construction of these representations is algebraic, based on the Gelfand-Naimark-Segal…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
The geometry of spaces with indefinite inner product, known also as Krein spaces, is a basic tool for developing Operator Theory therein. In the present paper we establish a link between this geometry and the algebraic theory of…
By applying an integral representation for $q^{k^{2}}$ we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of $q$-functions and polynomials that…
We study the Bergman kernel of certain domains in $\mathbb{C}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational…
We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type…
We give a general inequality for Bergman kernels of Bergman spaces defined by convex weights in $\C^n$. We also discuss how this can be used in Nazarov's proof of the Bourgain-Milman theorem, as a substitute for H\"ormander's estimates for…
We provide an introduction of some basic facts of uniformly almost periodic functions, such as Fourier series representations. A result is then proved about Fourier coefficients which is a generalization of the purely periodic case. We then…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
Fourier transforms of Lorentz invariant functions in Minkowski space, with support on both the timelike and the spacelike domains are performed by means of direct integration. The cases of 1+1 and 1+2 dimensions are worked out in detail,…
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental importance in the theoretical underpinning of kernel methods in…
Given a semisimple Lie algebra $\mathfrak{g}$, we can represent invariants of tensor products of fundamental representations of the quantum enveloping algebra $U_q(\mathfrak{g})$ using particular directed graphs called webs. In particular…
We introduce multi-sheeted versions of algebraic domains and quadrature domains, allowing them to be branched covering surfaces over the Riemann sphere. The two classes of domains turn out to be the same, and the main result states that the…
Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the sixth paper, exact analysis of the wave propagation in a beam with rectangular…
We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie…
This is a brief review of several algebraic constructions related to generalized fermionic spectra, of the type which appear in integrable quantum spin chains and integrable quantum field theories. We discuss the connection between…
In this article we construct Weil representations of quasi-split unitary groups $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associated to quadratic extensions of finite fields. We define these representations by using an adequate presentation…
We present a general derivation of semi-fermionic representation for generators of SU(N) group as a bilinear combination of Fermi operators. The constraints are fulfilled by means of imaginary Lagrange multipliers. The important case of…
We define left and right kernels of representations of Hopf algebras. In the case of group algebras, left and right kernels coincide and they are the usual kernels of modules. In the general case we show that these kernels coincide with the…