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Deformed Heisenberg algebra with reflection and d -orthogonal polynomials

Fethi Bouzeffour, Hanen Ben Mansour, Ali Zaghouani (2017)

Czechoslovak Mathematical Journal

This paper is devoted to the study of matrix elements of irreducible representations of the enveloping deformed Heisenberg algebra with reflection, motivated by recurrence relations satisfied by hypergeometric functions. It is shown that the matrix elements of a suitable operator given as a product of exponential functions are expressed in terms of d -orthogonal polynomials, which are reduced to the orthogonal Meixner polynomials when d = 1 . The underlying algebraic framework allowed a systematic derivation...

Derivation of the Hille-Hardy type formulae and operational methods

Giuseppe Dattoli (2003)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The Hille-Hardy formula is a bilinear generating function, involving products of Laguerre polynomials. We use the point of view, developed in previous publications, to propose an operational method which allows a fairly direct derivation of this kind of formulae.

Dispersive and Strichartz estimates on H-type groups

Martin Del Hierro (2005)

Studia Mathematica

Our purpose is to generalize the dispersive inequalities for the wave equation on the Heisenberg group, obtained in [1], to H-type groups. On those groups we get optimal time decay for solutions to the wave equation (decay as t - p / 2 ) and the Schrödinger equation (decay as t ( 1 - p ) / 2 ), p being the dimension of the center of the group. As a corollary, we obtain the corresponding Strichartz inequalities for the wave equation, and, assuming that p > 1, for the Schrödinger equation.

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