Investigations of the accuracy of approximations of semigroups ; Pusgrupių aproksimacijų tikslumo tyrimai

VILNIUS UNIVERSITYMonika Vilkiene˙INVESTIGATIONS OF THE ACCURACY OF APPROXIMATIONS OFSEMIGROUPSDoctoral dissertationPhysical sciences, mathematics (01 P)Vilnius, 2011The dissertation was prepared at Institute of Mathematics and Informatics in 2006–2010.Scientific supervisorDr. Habil. Vidmantas BENTKUS (Institute of Mathematics and Informatics, physicalsciences, mathematics – 01P).VILNIAUS UNIVERSITETASMonika Vilkiene˙PUSGRUPIU˛ APROKSIMACIJU˛ TIKSLUMO TYRIMAIDaktaro disertacijaFiziniai mokslai, matematika (01 P)Vilnius, 2011Disertacija rengta 2006–2010 metais Matematikos ir informatikos institute.Mokslinis vadovas:habil. dr. Vidmantas BENTKUS (Matematikos ir informatikos institutas, fiziniaimokslai, matematika – 01P).AbstractIn this thesis we investigate the convergence of Euler’s and Yosida approximations ofoperator semigroups. We obtain asymptotic expansions for Euler’s appro ofsemigroups with optimal bounds for the remainder terms. We provide various explicitformulas for the coefficients for these expansions. For Yosida approximations of semi-groups we obtain two optimal error bounds with optimal constants. We also constructasymptotic expansions for Yosida approximations of semigroups and provide optimalbounds for the remainder terms of these expansions.Reziume˙Disertacijoje tiriamas operatoriu˛ pusgrupiu˛ Eulerio ir Josidos aproksimaciju˛ konvergavi-mas.