ON FREQUENTLY HYPERCYCLIC C-DISTRIBUTION COSINE FUNCTIONS IN FRECHET SPACES

About Subspace-Frequently Hypercyclic Operators

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Difference sets and frequently hypercyclic weighted shifts

We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on l(Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently...

The Group Reduction for Bounded Cosine Functions on Umd Spaces

It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A)1/2 generates a bounded C0-group. The proof uses a transference principle for cosine functions.

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...

Convoluted C-cosine Functions and Convoluted C-semigroups