Spectral analysis of two doubly infinite Jacobi matrices with exponential entries

Autor:	František Štampach, Mourad E. H. Ismail
Rok vydání:	2019
Předmět:	Entire function 010102 general mathematics Function (mathematics) 01 natural sciences Exponential function Ramanujan's sum Combinatorics symbols.namesake Orthogonality 0103 physical sciences symbols Spectral analysis 010307 mathematical physics 0101 mathematics Analysis Mathematics
Zdroj:	Journal of Functional Analysis. 276:1681-1716
ISSN:	0022-1236
Popis:	We provide a complete spectral analysis of all self-adjoint operators acting on l 2 ( Z ) which are associated with two doubly infinite Jacobi matrices with entries given by q − n + 1 δ m , n − 1 + q − n δ m , n + 1 and δ m , n − 1 + α q − n δ m , n + δ m , n + 1 , respectively, where q ∈ ( 0 , 1 ) and α ∈ R . As an application, we derive orthogonality relations for the Ramanujan entire function and the third Jackson q-Bessel function.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a6525892557cb5feaacc6baa99eaf7d0 https://doi.org/10.1016/j.jfa.2018.12.010 Zobrazit plný text záznamu Full Text from ScienceDirect