Fractional powers of a difference operator

✍ Scribed by M.E.H. Ismail

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 285 KB
• Volume: 33
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(96)00226-x

✦ Synopsis

We use Fourier series to establish an integral representation of a right inverse of a difference operator which is the q-analogue of d. The kernel of this integral operator is ~/~4 and is the Rienmann mapping function that maps conformally the interior of an ellipse onto the open unit disc. We also define fractional powers of the right inverse operator and establish their index law.