Degenerate C-distribution cosine functions and degenerate C-ultradistribution cosine functions in locally convex spaces

Convoluted C-cosine Functions and Convoluted C-semigroups

Perturbation Theorems for Convoluted C-semigroups and Cosine Functions

Degenerate Multi-term Fractional Differential Equations in Locally Convex Spaces

We investigate, in the setting of sequentially complete locally convex spaces, degenerate multi-term fractional differential equations with Caputo derivatives. The obtained theoretical results are illustrated with some examples.

Integrated Cosine Functions

In order to the second order Cauchy problem (CP2): x"(t) Ax(t), z(O) z E D(A"), z"(O) y D(A") on a Banach space, Arendt and Kellermann recently introduced the integrated cosine function. This paper is concerned with its basic theory, which contain some properties, perturbation and approximation theorems, the relationship to analytic integrated semigroups, interpolation and extrapolation theorems.

Integration and approximation in cosine spaces of smooth functions

We study multivariate integration and approximation for functions belonging to a weighted reproducing kernel Hilbert space based on half-period cosine functions in the worst-case setting. The weights in the norm of the function space depend on two sequences of real numbers and decay exponentially. As a consequence the functions are infinitely often differentiable, and therefore it is natural to...