相关论文: Fredholm conditions for invariant operators: finit…

Thoma's theorem states that a group algebra $C^*(\Gamma)$ is of type I if and only if $\Gamma$ is virtually abelian. We discuss here some similar questions for the quantum groups, our main result stating that, under suitable virtually…

We study a system of pseudodifferential equations that is elliptic in the sense of Petrovskii on a closed compact smooth manifold. We prove that the operator generated by the system is Fredholm one on a refined two-sided scale of the…

The minimal operator and the maximal operator of an elliptic pseudo-differential operator with symbols on $\Z^n\times \mathbb{T}^n$ are proved to coincide and the domain is given in terms of a Sobolev space. Ellipticity and Fredholmness are…

We use algebras of pseudodifferential operators on groupoids to study geometric operators on non-compact manifolds and singular spaces. The first step is to establish that the geometric operators are in our algebras. This then leads to…

This paper is devoted to the space of unbounded Fredholm operators equipped with the graph topology, the subspace of operators with compact resolvent, and their subspaces consisting of self-adjoint operators. Our main results are the…

Markov processes are well understood in the case when they take place in the whole Euclidean space. However, the situation becomes much more complicated if a Markov process is restricted to a domain with a boundary, and then a satisfactory…

We provide a new type of proof for known or new Gohberg lemmas for pseudodifferential operators on Abelian locally compact groups $\mathrm{X}$. We use $C^*$-algebraic techniques, which also give spectral results to which the Gohberg lemma…

We prove an entropy formula for certain expansive actions of a countable discrete residually finite group $\Gamma $ by automorphisms of compact abelian groups in terms of Fuglede-Kadison determinants. This extends an earlier result proved…

We consider the operator algebra generated by pseudodifferential operators on a closed smooth surface and shift operator induced by a Morse--Smale diffeomorphism of this surface. Elements in this algebra are considered as operators in the…

We prove the spectral mapping theorem $\sigma_e(A_\phi) = \phi(\sigma_e(A_z))$ for the Fredholm spectrum of a truncated Toeplitz operator $A_\phi$ with symbol $\phi$ in the Sarason algebra $C+H^\infty$ acting on a coinvariant subspace…

We consider a Laplace type problem with a generalized impedance boundary condition of the form $\partial_\nu u=-\partial_x(g\partial_xu)$ on a flat part $\Gamma$ of the boundary. Here $\nu$ is the outward unit normal vector to…

The aim of this paper is to deal with the elliptic pdes involving a nonlinear integrodifferential operator, which are possibly degenerate and covers the case of fractional $p$-Laplacian operator. We prove the existence of a solution in the…

We investigate pseudodifferential operators on arbitrary locally compact abelian groups. As symbol classes for the Kohn-Nirenberg calculus we introduce a version of Sjoestrand's class. Pseudodifferential operators with such symbols form a…

Let $M$ be a compact boundaryless Riemannian manifold, carrying an effective and isometric action of a torus $T$, and $P_0$ an invariant elliptic classical pseudodifferential operator on $M$. In this note, we strengthen asymptotics for the…

In this paper. we study properties such as $L^r$-boundedness, compactness, belonging to Schatten classes and nuclearity, Riesz spectral theory, Fredholmness, ellipticity and Gohberg's lemma, among others, for pseudo-differential operators…

In this paper, we study elements of symbolic calculus for pseudo-differential operators associated with the weighted symbol class $M_{\rho, \Lambda}^m(\mathbb{ T}\times \mathbb{Z})$ (associated to a suitable weight function $\Lambda$ on…

We study elliptic theory on manifolds with boundary represented as a covering space. Firstly, we consider boundary value problems, where the boundary conditions are allowed to mix the values of functions in the fibers of the covering. We…

A Banach space operator $A\in B({\cal{X}})$ is polaroid, $A\in {\cal{P}}$, if the isolated points of the spectrum $\sigma(A)$ are poles of the operator; $A$ is hereditarily polaroid, $A\in{\cal{HP}}$, if every restriction of $A$ to a closed…

We consider the $3-D$ Dirac operator $\mathfrak{D}_{\boldsymbol{A},\Phi ,Q_{\sin }}$ with variable regular magnetic and electrostatic potentials $ \boldsymbol{A}$,$\Phi $ and with singular potentials $Q_{\sin }$ with support on a smooth…

We prove the spectral invariance of the algebra of classical pseudodifferential boundary value problems on manifolds with conical singularities in the Lp-setting. As a consequence we also obtain the spectral invariance of the classical…