On Averaging of One-Parameter Semigroups and Their Generators

The talk discusses methods for averaging one-parameter semigroups and their generators, focusing on random unbounded operators in Hilbert spaces. Key findings include the construction of generalized expectations through Chernoff equivalence, illustrative examples for resolvent and semigroup averaging, and the role of Feynman formulas in approximating quantum evolution operators. The results highlight the flexibility and limitations of these methods, offering insights into their use in dissipative dynamics, quantization ambiguities, and stochastic differential equations in mathematical physics.