Second kind integral equations on the real line [Elektronische Ressource] : solvability and numerical analysis in weighted spaces / von Kai Haseloh

Second Kind Integral Equations on the Real Line:Solvability and Numerical Analysisin Weighted SpacesVomFachbereich Mathematikder Universit at Hannoverzur Erlangung des GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationvonDipl.-Math. Kai Haselohgeboren am 23. September 1974 in Bad Oeynhausen2004Referent: Prof. Dr. Schmidt-Westphal, Universit at HannoverKorreferent: Prof. Dr. S. N. Chandler-Wilde, University of Reading, UKTag der Promotion: 26. Mai 2004AbstractThe exact and numerical solution of integral equations taking the formR∞ x (s) v(s,t)x(t)dt=y(s)incertainweightedsubspacesX ofthew ∞spaceX :=BC(R)(ofboundedandcontinuousfunctionsoverR)isstud-ied. Here, X denotes the weighted space of all functions x∈X satisfy-wing|w(s)x(s)|=O(1) as|s|→∞, for some weight function w1. Thekernel v is assumed to satisfy the simple condition|v(s,t)||(s t)|,1for some ∈L (R).Conditions on v and w are obtained, which ensure that the integral op-erator K in above equation is bounded on X and X . These conditionsware then strengthened to imply the equivalence of the spectrum (and es-sential spectrum) of K on X and X as well as several other statementswabout the solvability of the above integral equation.NSimilarboundednessandspectralresultsareshownfortheoperatorsKarising from suitable quadrature approximations of the integral op-erator K.