Théorèmes ergodiques multidimensionnels et suites aléatoires universellement représentatives en moyenne
Our aim is to prove that for any fixed 1/2 < α < 1 there exists a Hilbert space contraction T such that σ(T) = 1 and . This answers Zemánek’s question on the time regularity property.
We construct the fundamental solution of for functions q with a certain integral space-time relative smallness, in particular for those satisfying a relative Kato condition. The resulting transition density is comparable to the Gaussian kernel in finite time, and it is even asymptotically equal to the Gaussian kernel (in small time) under the relative Kato condition. The result is generalized to arbitrary strictly positive and finite time-nonhomogeneous transition densities on measure spaces. We...
If ϕ is an analytic self-mapping of the unit disc D and if is the Hardy-Hilbert space on D, the composition operator on is defined by . In this article, we consider which Toeplitz operators satisfy
We give general theorems which assert that divergence and universality of certain limiting processes are generic properties. We also define the notion of algebraic genericity, and prove that these properties are algebraically generic as well. We show that universality can occur with Dirichlet series. Finally, we give a criterion for the set of common hypercyclic vectors of a family of operators to be algebraically generic.