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Integral Equations and Operator Theory

, Volume 77, Issue 2, pp 149–166 | Cite as

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

  • Crispin Herrera Yañez
  • Egor A. Maximenko
  • Nikolai Vasilevski
Article

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,
$$\lim_{\frac{x}{y} \to 1} \left|f(x) - f(y)\right| = 0.$$

Mathematics Subject Classification (2010)

Primary 47B35 Secondary 47B32 32A36 44A10 44A15 

Keywords

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

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  • Crispin Herrera Yañez
    • 1
  • Egor A. Maximenko
    • 2
  • Nikolai Vasilevski
    • 1
  1. 1.Departamento de MatemáticasCINVESTAVMéxicoMéxico
  2. 2.Escuela Superior de Física y MatemáticasInstituto Politécnico NacionalMéxicoMéxico

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