Vertical Toeplitz Operators on the Upper Half-Plane and Very Slowly Oscillating Functions

Crispin Herrera Yañez, Egor A. Maximenko, Nikolai Vasilevski

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

We consider the C*-algebra generated by Toeplitz operators acting on the Bergman space over the upper half-plane whose symbols depend on the imaginary part of the argument only. Such algebra is known to be commutative, and is isometrically isomorphic to an algebra of bounded complex-valued functions on the positive half-line. In the paper we prove that the latter algebra consists of all bounded functions f that are very slowly oscillating in the sense that the composition of f with the exponential function is uniformly continuous or, in other words.

Original languageEnglish
Pages (from-to)149-166
Number of pages18
JournalIntegral Equations and Operator Theory
Volume77
Issue number2
DOIs
StatePublished - Oct 2013

Keywords

  • Bergman space
  • Laplace transform
  • Toeplitz operators
  • invariant under horizontal shifts
  • very slowly oscillating functions

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