Quasi-parabolic Composition Operators on Weighted Bergman Spaces

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COMPLEX ANALYSIS AND OPERATOR THEORY, vol.12, no.1, pp.55-79, 2018 (SCI-Expanded) identifier identifier


In this work we study the essential spectra of composition operators on weighted Bergman spaces of analytic functions which might be termed as "quasi-parabolic." This is the class of composition operators on with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form , where and . We especially examine the case where is discontinuous at infinity. A similar method used in Gul (J Math Anal Appl 377:771-791, 2011) for Hardy spaces is used 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.