In this paper, we investigate a class of abstract degenerate fractional differential equations with Caputo derivatives. We consider subordinated fractional resolvent families generated by multivalued linear operators, which do have removable singularities at the origin. Semi-linear degenerate fractional Cauchy problems are also considered in this context.
We study a new class of Markov type semigroups (not strongly continuous in general) in the space of all real, uniformly continuous and bounded functions on a separable metric space E. Our results allow us to characterize the generators of Markov transition semigroups in infinite dimensions such as the heat and the Ornstein-Uhlenbeck semigroups.
We study existence, uniqueness and form of solutions to the equation where α, β, γ and f are given, and stands for the even part of a searched-for differentiable function g. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.
We show that every abelian Polish group is the topological factor group of a closed subgroup of the full unitary group of a separable Hilbert space with the strong operator topology. It follows that all orbit equivalence relations induced by abelian Polish group actions are Borel reducible to some orbit equivalence relations induced by actions of the unitary group.
Let be a strongly continuous d-dimensional semigroup of linear contractions on , where (Ω,Σ,μ) is a σ-finite measure space and X is a reflexive Banach space. Since , the adjoint semigroup becomes a weak*-continuous semigroup of linear contractions acting on . In this paper the local ergodic theorem is studied for the adjoint semigroup T*. Assuming that each T(u), , has a contraction majorant P(u) defined on , that is, P(u) is a positive linear contraction on such that almost everywhere...