Deformed Heisenberg algebra with reflection and -orthogonal polynomials
Fethi Bouzeffour; Hanen Ben Mansour; Ali Zaghouani
Czechoslovak Mathematical Journal (2017)
- Volume: 67, Issue: 1, page 57-71
- ISSN: 0011-4642
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topBouzeffour, Fethi, Ben Mansour, Hanen, and Zaghouani, Ali. "Deformed Heisenberg algebra with reflection and $d$-orthogonal polynomials." Czechoslovak Mathematical Journal 67.1 (2017): 57-71. <http://eudml.org/doc/287931>.
@article{Bouzeffour2017,
abstract = {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 of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.},
author = {Bouzeffour, Fethi, Ben Mansour, Hanen, Zaghouani, Ali},
journal = {Czechoslovak Mathematical Journal},
keywords = {$d$-orthogonal polynomials; matrix element; coherent state; hypergeometric function; Meixner polynomials; $d$-dimensional linear functional vector},
language = {eng},
number = {1},
pages = {57-71},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Deformed Heisenberg algebra with reflection and $d$-orthogonal polynomials},
url = {http://eudml.org/doc/287931},
volume = {67},
year = {2017},
}
TY - JOUR
AU - Bouzeffour, Fethi
AU - Ben Mansour, Hanen
AU - Zaghouani, Ali
TI - Deformed Heisenberg algebra with reflection and $d$-orthogonal polynomials
JO - Czechoslovak Mathematical Journal
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 67
IS - 1
SP - 57
EP - 71
AB - 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 of the recurrence relations, difference equation, lowering and rising operators and generating functions which these polynomials satisfy.
LA - eng
KW - $d$-orthogonal polynomials; matrix element; coherent state; hypergeometric function; Meixner polynomials; $d$-dimensional linear functional vector
UR - http://eudml.org/doc/287931
ER -
References
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