Related papers: Generation of semigroups for vector-valued pseudod…
In this paper, we consider pseudodifferential operators on the torus with operator-valued symbols and prove continuity properties on vector-valued toroidal Besov spaces, without assumptions on the underlying Banach spaces. The symbols are…
The aim of this paper is twofold. On one hand, generalizing some recent results obtained in the quaternionic setting, but using simpler techniques, we prove the generation theorems for semigroups in Banach spaces whose set of scalars…
In this article we study a class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts. Toroidal symbols are investigated and the correspondence…
The present paper, is devoted to investigation of operator--valued Fourier multiplier theorems from $B_{q_{1},r}^{s}$ to $B_{q_{2},r}^{s}$, optimal embedding of Besov spaces, the separability and positivity of differential operators. Here,…
Following previous works for the unit ball, we define quasi-radial pseudo-homogeneous symbols on the projective space and obtain the corresponding commutativity results for Toeplitz operators. A geometric interpretation of these symbols in…
Specific global symbol classes and corresponding pseudodifferential operators of infinite order that act continuously on the space of tempered ultradistributions of Beurling and Roumieu type are constructed. For these classes, symbolic…
We prove that in a large class of Banach spaces of analytic functions in the unit disc $\mathbb{D}$ an (unbounded) operator $Af=G\cdot f'+g\cdot f$ with $G,\, g$ analytic in $\mathbb{D}$ generates a $C_0$-semigroup of weighted composition…
We search for pseudo-differential operators acting on holomorphic Sobolev spaces. The operators should mirror the standard Sobolev mapping property in the holomorphic analogues. The setting is a closed real-analytic Riemannian manifold, or…
We extend the Ruzhansky-Turunen theory of pseudo differential operators on compact Lie groups into a tool that can be used to investigate group-valued Markov processes in the spirit of the work in Euclidean spaces of N.Jacob and…
We construct a new bounded functional calculus for the generators of bounded semigroups on Hilbert spaces and generators of bounded holomorphic semigroups on Banach spaces. The calculus is a natural (and strict) extension of the classical…
The reappearance of a sometimes called exotic behavior for linear and multilinear pseudodifferential operators is investigated. The phenomenon is shown to be present in a recently introduced class of bilinear pseudodifferential operators…
We develop a geometric framework for Weyl quantization on pseudo-Riemannian manifolds, in which pseudodifferential operators act on sections of vector bundles equipped with arbitrary connections. We construct the associated star product and…
We introduce some general classes of pseudodifferential operators with symbols admitting exponential type growth at infinity and we prove mapping properties for these operators on Gelfand-Shilov spaces both in the quasi-analytic and in the…
We present a spectral mapping theorem for continuous semigroups of operators on any Banach space $E$. The condition for the hyperbolicity of a semigroup on $E$ is given in terms of the generator of an evolutionary semigroup acting in the…
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…
We discuss the construction of the full Sobolev (H\"older) scale for non-densely defined operators on a Banach space with rays of minimal growth. In particular, we give a construction for extrapolation- and Favard spaces of generators of…
In this work I investigate uniformly continuous semigroups of sublinear transition operators on the Banach space of bounded real-valued functions on some countable set. I show how the family of exponentials of a bounded sublinear rate…
We consider a semigroup of operators in the Banach space $C_b(H)$ of uniformly continuous and bounded functions on a separable Hilbert space $H$. In particular, we deal with semigroups that are related to solution of stochastic PDEs in $H$…