We study semigroups generated by general fractional Ornstein–Uhlenbeck operators acting on $$L^2({\mathbb {R}}^n)$$ . characterize geometrically the partial Gevrey-type smoothing properties of these semigroups, and we sharply describe blow-up associated seminorms for short times, generalizing hypoelliptic quadratic cases. As a byproduct this study, establish subelliptic estimates enjoyed whole ...

C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss...

We consider different realizations of the operators Lθ,a u(x) := xu(x) + (ax + θx)u(x), θ ∈ R, a ∈ R, acting on suitable spaces of real valued continuous functions. The main results deal with the existence of Feller semigroups generated by Lθ,a and the representation Lθ,a = G 2 a + θGa, where Gau = xu, 0 ≤ a ≤ 1, generates a (not necessarily strongly continuous) group. Explicit formulas of the ...

We investigate selfadjoint C0-semigroups on Euclidean domains satisfying Gaussian upper bounds. Major examples are semigroups generated by second order uniformly elliptic operators with Kato potentials and magnetic fields. We study the long time behaviour of the L∞ operator norm of the semigroup. As an application we prove a new L∞-bound for the torsion function of a Euclidean domain that is cl...

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.

In this paper we characterize the Banach lattices with Hardy-Littlewood property by using maximal operators defined semigroups of associated inverse Gauss measure.

A collection F of operators on a vector space V is said to be semitransitive if for every pair of nonzero vectors x and y in V there exists a member T of F such that either Tx = y or Ty = x (or both). We study semitransitive algebras and semigroups of operators. One of the main results is that if the underlying field is algebraically closed, then every semitransitive algebra of operators on a s...

be linear and quasilinear evolution equations of parabolic type in a Banach space X respectively. By "parabolic type" we mean that A(t) and A(t,u) are all the infinitesimal generators of analytic linear semigroups on X we do not necessarily assume that the domains of the operators A(t) and A("t,u) are dense subspaces of X, so the semigroups generated by them may not be of class c0 J. The domain...

We use an intrinsic metric type approach to investigate when C0-semigroups generated by second order elliptic differential operators are stochastic. We give a new condition for stochasticity that encompasses the volume growth conditions by Karp and Li and by Perelmuter and Semenov. MSC 2000: 47D07, 35J15, 47B44