on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it characterizes disjoint frequent hypercyclicity for family of unilateral pseudo-shifts on c0(N) ?p(N), 1?p<?. As an application, we characterize frequently hypercyclic weighted shifts. give analogous results the weaker notions upper reiterative hypercyclicity. Finally, provide counterexamples showing that, although hypercycl...