Please use this identifier to cite or link to this item:
http://142.54.178.187:9060/xmlui/handle/123456789/8459
Title: | PSEUDORESOLVENTS AND SEMIGROUPS |
Authors: | Awan, Abdul Sami |
Keywords: | Natural Sciences |
Issue Date: | 2004 |
Publisher: | GC University, Lahore, Pakistan. |
Abstract: | The notions of resolvent, pseudoresolvent and a few results along with some re- markable properties are recalled. A new concept, the L ∞ -type pseudoresolvent is introduced. The aim of this work is firstly to give a characterization theorem for L ∞ -type pseudoresolvents and for the generators of L ∞ -type pseudoresolvents. Moreover, the connection between the L ∞ -type pseudoresolvents and C 0 -equicontinuous semigroups is pointed out. Secondly, the main part of this work is devoted to approximation of pseudoresol- vents and their generators. If R n , R : Λ → L(X), n ≥ 1 are generated pseudoresol- vents and A n , A their generators, then it is investigated under which conditions A is approximated by A n and R is approximated by R n , n ≥ 1. In addition, the conditions under which a sequence of generated pseudoresolvents approximates a pseudoresolvent are given, and in this case the connection between generators is studied. In the last chapter we have proved a theorem of characterization for exponentially bounded semigroups. To any exponentially bounded semigroup we have associated a projective family of semigroups acting on Banach spaces. |
URI: | http://142.54.178.187:9060/xmlui/handle/123456789/8459 |
Appears in Collections: | Thesis |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.