Abstract/Details

On some formulas of W.Gosper and spectral properties of certain operators in weighted spaces

Zhang, Ruiming. 
 University of South Florida ProQuest Dissertations Publishing,  1993. 9323706.

Abstract (summary)

By using his path invariant method and the symbolic algebra package Macsyma, R. William Gosper discovered many interesting identities. In Chapter 1 we prove some of them in a more conventional way and use our approach to prove some of his conjectures. It turned out that what is behind some of the summations are one-step iterations and what is behind some of the continued fraction identities are 3 term recurrence relations.

It is known that most general classical orthogonal polynomials are Askey-Wilson polynomials. They satisfy a second order equation in ${\cal D}\sb{q}$, ${\cal D}\sb{q}$ being the Askey-Wilson operator. This naturally led to the question of investigating special properties of ${\cal D}\sb{q}$ in various weighted spaces. In Chapter 2, we consider the operator $D={d\over dx}$, on the ultraspherical space $L\sp2\lbrack (1-x\sp2)\sp{\nu-1/2}dx$) and the Jacobi space $L\sp2\lbrack (1-x\sp\alpha)(1+x)\sp\beta dx$). The point spectra are zeros of Bessel functions of the first kind and zeros of Coulomb function respectively. We find the point spectrum of ${\cal D}\sb{q}$ to be the set of zeros of Jackson q Bessel functions. We also have a new q-generalization of the exponential function and some new expansion in terms of q-ultraspherical polynomials.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Gosper, [email protected]; Jacobi polynomials
Title
On some formulas of W.Gosper and spectral properties of certain operators in weighted spaces
Author
Zhang, Ruiming
Number of pages
58
Degree date
1993
School code
0206
Source
DAI-B 54/04, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-208-41161-2
Advisor
Ismail, Mourad E. H.
University/institution
University of South Florida
University location
United States -- Florida
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9323706
ProQuest document ID
304058228
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/304058228