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Rational Approximation Schemes For Solutions Of Abstract Cauchy Problems And Evolution Equations, Patricio Gabriel Jara

LSU Doctoral Dissertations

In this dissertation we study time and space discretization methods for approximating solutions of abstract Cauchy problems and evolution equations in a Banach space setting. Two extensions of the Hille-Phillips functional calculus are developed. The first result is the Hille-Phillips functional calculus for generators of bi-continuous semigroups, and the second is a C-regularized version of the Hille-Phillips functional calculus for generators of C-regularized semigroups. These results are used in order to study time discretization schemes for abstract Cauchy problems associated with generators of bi-continuous semigroups as well as C-regularized semigoups. Stability, convergence results, and error estimates for rational approximation schemes …