Open AccessOrthogonality and Completeness of $q$-Fourier Type Systems
Author(s) -
Mourad E. H. Ismail
Publication year - 2001
Publication title -
zeitschrift für analysis und ihre anwendungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.567
H-Index - 35
eISSN - 1661-4534
pISSN - 0232-2064
DOI - 10.4171/zaa/1044
Subject(s) - completeness (order theory) , orthogonality , fourier transform , type (biology) , mathematics , mathematical analysis , geology , geometry , paleontology
We establish orthogonality and completeness of the system of q-exponential functions {Eq(· ; iωn)} using orthogonality and dual orthogonality of a q-analogue of Lommel polynomials. We also set up a very general procedure by which one can produce similar orthogonal systems using bilinear generating functions formed by products of two complete orthogonal function systems.
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom