Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions

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Abstract

In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as “quasi-parabolic.” This is the class of composition operators on H2 with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form φ(z)=z+ψ(z), where and (ψ(z))>>0. We especially examine the case where ψ is discontinuous at infinity. A new method is devised to show that this type of composition operator fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra.

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• Essential spectra of quasi-parabolic composition operators on hardy spaces of analytic functions. (deposited 07 Dec 2010 22:35)
  • Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions. (deposited 22 Mar 2011 14:38) [Currently Displayed]