Invertibility of a class of Toeplitz operators over the half plane [Elektronische Ressource] / vorgelegt von Vladimir Vasilyev

Invertibility of a Class of ToeplitzOperators over the Half Planevon der Fakultat fur Mathematik der Technischen Universitat ChemnitzgenehmigteDissertationzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegt von M.Sc. Vladimir A. Vasilyevgeboren am 24. August 1978 in Stavropol (Russland)eingereicht am 28.09.2006Gutachter: Prof. Dr. B. Silbermann, TU ChemnitzProf. Dr. V.S. Rabinovich,Instituto Politecnico Nacional, MexicoProf. Dr. F.-O. Speck, Instituto Superior Tecnico, PortugalTag der Verteidigung: 07.02.2007Bibliographic descriptionVasilyev, Vladimir AlexandrovichInvertibility of a Class of Toeplitz Operators over the Half PlaneDissertation (in English), 100 pages, Technical University of Chemnitz,Faculty of Mathematics, Chemnitz, 2006.AbstractThis paper is concerned with invertibility and one-sided invertibility of Toeplitz operatorsover the half plane, whose symbols admit homogenous discontinuities, and with stabilityof their pseudo nite sections.The invertibility of this class of Toeplitz operators is studied using the related algebrainvolving certain composition operators. The related stability problem plays here an im-portant role. The invertibility criterium is given in terms of invertibility of a family of onedimensional Toeplitz operators.