Related papers: Solvability of a class of evolution operators on c…

The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…

We consider the observability problem for non-autonomous evolution systems (i.e., the operators governing the system depend on time). We introduce an averaged Hautus condition and prove that for skew-adjoint operators it characterizes exact…

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…

Let $G$ be an algebraic group and let $X$ be a smooth $G$-variety with two orbits: an open orbit and a a closed orbit of codimension $1$. We give an algebraic description of the category of $G$-equivariant vector bundles on $X$ under a mild…

We study the Cauchy problem for a class of third order linear anisotropic evolution equations with complex valued lower order terms depending both on time and space variables. Under suitable decay assumptions for $|x| \to \infty$ on these…

In this paper we prove reducibility of classes of linear first order operators on tori by applying a generalization of Moser's theorem on straightening of vector fields on a torus. We consider vector fields which are a $C^\infty$…

The description of the Paley-Wiener space for compactly supported smooth functions $C^\infty_c(G)$ on a semi-simple Lie group $G$ involves certain intertwining conditions that are difficult to handle. In the present paper, we make them…

We consider the Cauchy problem for a second-order evolution equation, in which the problem operator is the sum of two self-adjoint operators. The main feature of the problem is that one of the operators is represented in the form of the…

We consider three families of lattices on the oscillator group $G$, which is an almost nilpotent not completely solvable Lie group, giving rise to coverings $G \to M_{k, 0} \to M_{k, \pi} \to M_{k, \pi/2}$ for $k\in \Z$. We show that the…

We provide criteria for self-adjointness and {\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A…

We study the Cauchy problem for a class of linear evolution equations of arbitrary order with coefficients depending both on time and space variables. Under suitable decay assumptions on the coefficients of the lower order terms for $|x|$…

We consider the Cauchy problem for a $3$-evolution operator $P$ with $(t,x)$-depending coefficients and complex valued lower order terms. We assume the initial data to be Gevrey regular and to admit an exponential decay at infinity, that…

We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…

A solvmanifold is a compact differentiable manifold M on which a connected solvable Lie group G acts transitively. As the main result, we will see, applying a result of Arapura and Nori on solvable Kaehler groups and some of the author's…

Several classes of systems of evolution equations with one or two vector unknowns are considered. We investigate also systems with one vector and one scalar unknown. For these classes all equations having the simplest higher symmetry are…

We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…

In this paper we will first present some results about the local solvability property of a class of degenerate second order linear partial differential operators with smooth coefficients. The class under consideration (which in turn is a…

When the singular values of the evolution operator are all smaller or all greater than one, stable integration algorithms are obtained either by explicit or implicit methods. When the singular spectrum mixes greater and smaller than one…

A K3 category is by definition a Calabi-Yau category of dimension two. Geometrically K3 categories occur as bounded derived categories of (twisted) coherent sheaves on K3 or abelian surfaces. A K3 category is generic if there are no…

We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…