Mellin Transform, Monomial Symbols, and Commuting Toeplitz Operators

✍ Scribed by Zeljko Cucković; N.V. Rao

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 350 KB
• Volume: 154
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1997.3204

✦ Synopsis

In this paper we give necessary and sufficient conditions for a symbol that produces a Toeplitz operator on the Bergman space that commutes with another such operator whose symbol is a monomial. The result is stated in terms of the Mellin transform of the symbol. As a corollary, we show that a Toeplitz operator with a radial symbol may only commute with another such operator with a radial symbol.