Analytic Semigroup Approach to
Convolution Volterra Equations

By Kristina Willemina Homan
May 2003
Delft University Press
ISBN: 90-407-2396-6
141 pages, 6 1/2" x 9 1/2"
$54.00 Paper Original


Contents of this doctoral dissertation include: Preliminaries, Pointwise versions of solutions to Cauchy problems in Lp-Spaces, Scalar linear Volterra equations, Volterra equations in a separable Hilbert space, Stochastic linear Voltera equations. This thesis is concerned with Volterra integrodifferential equations of convolution type with completely monotonic kernels. The main objective is to provide an analytic semigroup setting for these equations, based on the complete monotonicity of the kernel. Bernstein's theorem allows rewriting the Volterra equation into an abstract Cauchy problem in an appropriate infinite dimensional Hilbert space, in such a way that the operator governing this problem generates an analytic semigroup.


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