Generalized convolution operators and asymptotic spectral theory [Elektronische Ressource] / vorgelegt von Olga Nikolaievna Zabroda

Generalized convolution operatorsand asymptotic spectral theoryvon der Fakultat fur Mathematik¨ ¨der Technischen Universitat Chemnitz¨genehmigteDissertationzur Erlangung des akademischen GradesDoctor rerum naturalium(Dr. rer. nat.)vorgelegt von Dipl.-Math. Olga Nikolaievna Zabrodageboren am 29. Oktober 1979 in Azov (Russland)eingereicht am 29.06.2006Gutachter: Prof. Dr. B. Silbermann, TU ChemnitzProf. Dr. T. Ehrhardt, University of California, Santa CruzProf. Dr. S. Grudsky, CINVESTAV, MexicoTag der Verteidigung: 11.12.2006Bibliographic descriptionZabroda, Olga NikolaievnaGeneralized convolution operators and asymptotic spectral theoryDissertation (in English), Chemnitz University of Technology,Department of Mathematics, Chemnitz, 2006138 pagesAbstractThe present dissertation contributes to the further advancement of the theory of variousclasses of discrete and continuous (integral) convolution operators. This is alreadyhighly developed. The most important questions in this theory are about the invertibilityofconvolutionoperators,abouttheconstructionoftheirinverses,andaboutthepropertiesof their spectra. These problems hardly allow an explicit description. In order to tacklethem in practice, one usually resorts to the finite section method.