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(Non-)Autonomous Cauchy Problems and Product Formula Approximation for Propagators

Mathematical Physics & Probability

Speaker: Valentin A. Zagrebnov, Institut de Mathématiques de Marseille (UMR 7373) and Université d'Aix-Marseille, France
Location: 2112 MSB
Start time: Wed, Feb 24 2016, 4:10PM

For autonomous Cauchy problem this lecture reviews the Trotter-Kato product formula approximation for strongly continuous and Gibbs semigroups in the operator-norm and the trace-norm topologies, including the rate of convergence in a Hilbert space.

For non-autonomous well-posed Cauchy problems, after review of results about construction of the corresponding strongly continuous evolution families (propagators) via product formula approximations in the strong operator topology, we discuss the operator-norm error-bound for convergence of these approximations in Hilbert and Banach spaces.