Related papers: Ursell operators in statistical physics I: general…
We study in more detail the properties of the generalized Beth Uhlenbeck formula obtained in a preceding article. This formula leads to a simple integral expression of the grand potential of the system, where the interaction potential…
In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the…
The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which…
General non-degenerate p-adic operators of ultrametric diffusion are introduced. Bases of eigenvectors for the introduced operators are constructed and the corresponding eigenvalues are computed. Properties of the corresponding dynamics…
We use a degeneration of the 1D double affine Hecke algebra and the Dunkl operator to study systematically nonsymmetric Bessel functions and their truncations.
We study degenerate hypoelliptic Ornstein-Uhlenbeck operators in $L^2$ spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate…
Based on operator algebras commonly used in quantum mechanics some properties of special functions such as Hermite and Laguerre polynomials and Bessel functions are derived.
In this paper, we aim to present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella hypergeometric functions, by using the extended Bessel function due to Boudjelkha [4].…
We give several new formulas which are useful for Schubert Calculus associated with the orthogonal groups and related orthogonal degeneracy loci.
For a degenerate hyperbolic equation of the second kind, and with a spectral parameter are studied the Cauchy problem, Cauchy-Goursat and Goursat in a new class of generalized solutions and is given an example that shows the importance of…
In order to enlarge the present arsenal of semiclassical toools we explicitly obtain here the Husimi distributions and Wehrl entropy within the context of deformed algebras built up on the basis of a new family of q-deformed coherent…
We study some basic properties of the class of universal operators on Hilbert space, and provide new examples of universal operators and universal pairs.
Finite dimensional representations of extended Weyl-Heisenberg algebra are studied both from mathematical and applied viewpoints. They are used to define unitary phase operator and the corresponding eigenstates (phase states). It is also…
In this paper, we show how a class of operators used in the analysis of measures from wavelets and iterated function systems may be understood from a special family of representations of Cuntz algebras.
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
The article discusses the fractional powers of the Bessel operator and their numerical implementation. An extensive literature is devoted to the study of fractional powers of the Laplace operator and their applications. Such degrees are…
In this paper we find explicit formulas for the Poisson and heat semigroups associated to the modified Bessel operator and on the hyperbolic spaces $\mathbb{H}^n$.