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On a class of abstract degenerate fractional differential equations of parabolic type

Marko Kostić (2018)

Commentationes Mathematicae Universitatis Carolinae

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.

On a class of discontinuous operators in Hilbert spaces

Sebastiano Boscarino (2003)

Commentationes Mathematicae Universitatis Carolinae

We construct a class of discontinuous operators in infinite-dimensional separable Hilbert spaces, answering a natural question which arises in comparing a fixed point theorem of Altman and Shinbrot ([1], [4]) with its improvement obtained by Ricceri ([2], [3]).

On a class of Markov type semigroups in spaces of uniformly continuous and bounded functions

Enrico Priola (1999)

Studia Mathematica

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.

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