Related papers: On the closure of elliptic wedge operators

In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for…

We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.

We consider special classes of linear bounded operators in Banach spaces and suggest certain operator variant of symbolic calculus. It permits to formulate an index theorem and to describe Fredholm properties of elliptic pseudo-differential…

In this paper we study quasilinear elliptic systems driven by so-called double phase operators and nonlinear right-hand sides depending on the gradients of the solutions. Based on the surjectivity result for pseudomonotone operators we…

We obtain a complete description of semi-Fredholm spectra of operators of the form $(Tf)(z) = w(z)f(B(z)$ acting on the disc algebra in the case when $B$ is either elliptic or double parabolic finite Blaschke product of degree $d \geq 2$…

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

Starting from the definition of A-Fredholm and semi-A-Fredholm operator on the standard module over a unital C*- algebra A, introduced in [8] and [4], we construct various generalizations of these operators and obtain several results as an…

We introduce a refined Sobolev scale on a vector bundle over a closed infinitely smooth manifold. This scale consists of inner product H\"ormander spaces parametrized with a real number and a function varying slowly at infinity in the sense…

We show that the multi--quasi-ellipticity is a necessary and sufficient condition for the property of elliptic iterates to be hold for multi-quasi-homogenous differential operators.

We show that the computation of the Fredholm index of a fully elliptic pseudodifferential operator on an integrated Lie manifold can be reduced to the computation of the index of a Dirac operator, perturbed by a smoothing operator,…

Let X be a smooth compact manifold with boundary. For smooth foliations on the boundary of X admitting a `resolution' in terms of a fibration, we construct a pseudodifferential calculus generalizing the fibred cusp calculus of Mazzeo and…

We show that, under certain regularity assumptions, there exists a linear extension operator.

We introduce and study {\it new} relative spectral invariants of {\it two} elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depend on both the eigenvalues and the…

Extensions of one-parameter operator semigroups on Archimedean vector lattices to their order/ru-completions are studied. Existence and uniqueness of the extension to the ru-completion is established in the class of positive semigroups. An…

We study the ergodic properties of Schr\"odinger operators on a compact connected Riemannian manifold $M$ without boundary in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…

We consider one-dimensional inhomogeneous parabolic equations with higher-order elliptic differential operators subject to periodic boundary conditions. In our main result we show that the property of continuous maximal regularity is…

For a Fedosov manifold (symplectic manifold equipped with a symplectic torsion-free affine connection $\nabla$) admitting a metaplectic structure, we shall investigate two sequences of first order differential operators acting on sections…

The notion of quasi boundary triples and their Weyl functions is an abstract concept to treat spectral and boundary value problems for elliptic partial differential equations. In the present paper the abstract notion is further developed,…

In this note semibounded self-adjoint extensions of symmetric operators are investigated with the help of the abstract notion of quasi boundary triples and their Weyl functions. The main purpose is to provide new sufficient conditions on…

We provide a simple proof of the Holonomy Theorem using a new Lyndon-Chiswell length function on the Karnofsky-Rhodes expansion of a semigroup. Unexpectedly, we have both a left and a right action on the Chiswell tree by elliptic maps.