Related papers: A class of pseudo-differential operators with osci…
Mixed-norm Lebesgue spaces found their place in the study of some questions in the theory of partial differential equations, as can be seen from recent interest in the continuity of certain classes of pseudodifferential operators on these…
We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.
In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…
Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a…
We give examples of fourth-order scattering-type operators, acting on $L_2(\mathbb{R})$, which have eigenvalues embedded in their continuous spectra.
We study spectral properties of a class of global infinite order pseudo-differential operators and obtain the asymptotic behaviour of the spectral counting functions of such operators. Unlike their finite order counterparts, their spectral…
Lecture notes for one of the courses at the OPSFA Summerschool 6, July 11-15, 2016. All the results in these notes have appeared in the literature. Many special functions are eigenfunctions to explicit operators, such as difference and…
We investigate the Schatten-von Neumann properties of pseudo-differential operators using the method proposed by A. Boulkhemair in \cite{Boulkhemair 2}. The symbols are elements of the ideals $S_{w}^{p}$ of the Sj\"ostrand algebra $S_{w}$.
In this article, we conduct a study of integral operators defined in terms of non-convolution type kernels with singularities of various degrees. The operators that fall within our scope of research include fractional integrals, fractional…
We study the numerical range of bounded linear operators on quaternionic Hilbert spaces and its relation with the S-spectrum. The class of complex operators on quaternionic Hilbert spaces is introduced and the upper bild of normal complex…
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…
In this paper, we consider the trace property of pseudo-differential operators with symbols in $\alpha$-modulation spaces.
We construct an abstract pseudodifferential calculus with operator-valued symbol, adapted to the treatment of Coulomb-type interactions, and we apply it to study the quantum evolution of molecules in the Born-Oppenheimer approximation, in…
In the scattering theory framework, we consider a pair of operators $H_0$, $H$. For a continuous function $\phi$ vanishing at infinity, we set $\phi_\delta(\cdot)=\phi(\cdot/\delta)$ and study the spectrum of the difference…
In this paper, we give a sharp sparse domination of pseudodifferential operators associated with symbols belonging to the H\"{o}rmander class, and fundamental solutions of dispersive equations. Furthermore, we give boundedness results of…
The paper discusses the spectrum of Toeplitz operators in Bargmann spaces. Our Toeplitz operators have real symbols with a variable sign and a compact support. A class of examples is considered where the asymptotics of the eigenvalues of…
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…
In this paper we study the action of pseudo-differential operators acting on Gevrey spaces. We introduce classes of classical symbols with spatial Gevrey regularity. As the spatial Gevrey regularity of a symbol $p(\cdot,\xi)$ may depend on…
Let $H_0$ and $H$ be self-adjoint operators in a Hilbert space. In the scattering theory framework, we describe the essential spectrum of the difference $\varphi(H)-\varphi(H_0)$ for piecewise continuous functions $\varphi$. This…
We introduce the new concepts of pseu\-do numerical range for operator functions and families of sesquilinear forms as well as the pseu\-do block numerical range for $n \times n$ operator matrix functions. While these notions are new even…