2001/01/25 by V. V. Borzov, Vadim V. Borzov, Borzov, Vadim V. +2
Mathematics · Physics and Astronomy · #05E35 (Primary) 05E35 (Secondary) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.CA #math.QA #msc:05E35
paper · pdf · doi:10.48550/arxiv.math/0101215
13 pages, no figures
arxiv created 2001/01/25 · openalex publication_date 2001/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work continues the research of generalized Heisenberg algebras connected with several orthogonal polynomial systems. The realization of the annihilation operator of the algebra corresponding to a polynomial system by a differential operator A is obtained. The important special case of orthogonal polynomial systems, for which the matrix of the operator A in l2(Z+) has only off-diagonal elements on the first upper diagonal different from zero, is considered. The known generalized Hermite polynomials give us an example of such orthonormal system. The replacement of the usual derivative by q-derivative allows us to use the suggested approach for similar investigation of various "deformed" polynomials.