Abstract:
This session continues the discussion on the connection between semigroups and equations
in Banach spaces, as well as applications to solving partial differential equations in finite-dimensional spaces. The informal meaning of the Chernoff theorem will be presented as an
infinite-dimensional analogue of the fundamental limit from elementary calculus. It will be
proven that the Laplace transform of the Chernoff approximations of a semigroup converges
to the resolvent of the semigroup's generator. As a corollary, Chernoff approximations for
solutions to differential equations with variable coefficients – both ordinary and elliptic partial
differential equations – will be derived.
