Some Results on Operator Semigroups and Evolution Problems

The specialized book "Some Results on Operator Semigroups and Evolution Problems" by András Serény offers a comprehensive analysis of questions that arise within the framework of functional-analytic investigations of dynamic systems and differential equations. The work addresses the operator-theoretic correspondences of central ergodic theoretical concepts such as strong and weak mixing. These concepts are associated with specific types of asymptotic behavior of operator semigroups in the weak operator topology. Furthermore, classical theorems by Halmos and Rohlin for measure-preserving transformations are transferred to the context of Hilbert space operators. The book illustrates the methods and results of operator semigroups using a class of telegraph systems with varying boundary conditions and examines both linear and nonlinear boundary value problems. It particularly emphasizes the stability of linear telegraph systems and the existence of solutions under time-dependent boundary conditions, an area that has been little explored so far.