Related papers: Multiplicative operators in the spaces of Schwartz…
This article introduces classes of normal and unitary operators on smooth Banach spaces, providing extensions of the classical notions of normal and unitary operators from Hilbert spaces to the smooth Banach space setting. The proposed…
Functions which are covariant or invariant under the transformations of a compact linear group $G$ acting in a euclidean space $\real^n$, can be profitably studied as functions defined in the orbit space of the group. The orbit space is the…
In this paper, we introduce a family of Fourier multipliers using the spherical Fourier transform on Gelfand pairs. We refer to them as spherical Fourier multipliers. We study certain sufficient conditions under which they are bounded.…
We define the doubling zeta integral for smooth families of representations of classical groups. Following this we prove a rationality result for these zeta integrals and show that they satisfy a functional equation. Moreover, we show that…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A smooth spectral density gives an explicit method to factorize the spectral density and compute the constituents of…
In this paper several joint spectra for a finite commuting family of closed operators in Banach space are considered, some new relations between these spectra established (earlier only the inclusion of the Taylor spectrum in the commutant…
Building on the work [18], where some standard basis for the queer $q$-Schur superalgebra $\mathcal{Q}_q(n,r;R)$ is defined by a labelling set of matrices and their associated double coset representatives, we investigate the matrix…
A new approach to normal operators in real Hilbert spaces is discussed, and a spectral representation is obtained, derived directly from the complex case. The results are then applied to quaternionic normal operators, regarded as a special…
The definitions of scattering matrix and inclusive scattering matrix in the framework of formulation of quantum field theory in terms of associative algebras with involution are presented. The scattering matrix is expressed in terms of…
The main aim of the present work is to arrive at a mathematical theory close to the historically original conception of generalized functions, i.e. set theoretical functions defined on, and with values in, a suitable ring of scalars and…
Smoothed Wigner transforms have been used in signal processing, as a regularized version of the Wigner transform, and have been proposed as an alternative to it in the homogenization and / or semiclassical limits of wave equations. We…
In this paper we begin a study of the space of unbounded self-adjoint Fredholm operators as a classifying space for K^{1}(X), with the goal of incorporating the information in the eigenspaces and eigenvalues of the operators. In particular,…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
By means of several examples, we motivate that universal properties are the simplest way to solve a given mathematical problem, explaining in this way why they appear everywhere in mathematics. In particular, we present the co-universal…
Schwartz functions, or measures, are defined on any smooth semi-algebraic ("Nash") manifold, and are known to form a cosheaf for the semi-algebraic restricted topology. We extend this definition to smooth semi-algebraic stacks, which are…
The theory of quantum symmetric pairs is applied to $q$-special functions. Previous work shows the existence of a family $\chi$-spherical functions indexed by the integers for each Hermitian quantum symmetric pair. A distinguished family of…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…