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Essential Spectra of Quasi-parabolic Composition Operators on Hardy Spaces of Analytic Functions | | Ugur Gul
; | | Date: |
24 Feb 2010 | | 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 H^{2} with symbols whose conjugate
with the Cayley transform on the upper half-plane are of the form phi(z) =
z+psi(z) where psiin H^{2}(mathbb{H}) and Im(psi(z)) >delta > 0. We
especially examine the case where psi is discontinuous at infinity. A new
method is devised to show that this type of composition operators 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. | | Source: | arXiv, 1002.4640 | | Services: | Forum | Review | PDF | Favorites | |
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