Related papers: Notes on generalized pseudo-differential operators
A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…
In this paper, we define differential graded vertex operator algebras and the algebraic structures on the associated Zhu algebras and $C_2$-algebras. We also introduce the corresponding notions of modules, and investigate the relations…
We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for…
The paper deals with a fractional derivative introduced by means of the Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
The Weyl-Sims classification for a second-order ordinary differential equation with general complex coefficients is investigated. Connections are then established between the associated m-function and the spectral properties of…
The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.
In this paper, we briefly explain the spectral expansion problem for differential operators defined on the entire real line, generated by a differential expression with periodic, complex-valued coefficients.
In this work we obtain sharp $L^p$-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis…
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give few results on diffeological principal bundles with (a priori) no local…
In this paper we consider shift operators, self-adjoint, unitary and normal operators on the standard module over a unital C*-algebra A. We define various generalized spectra in A of these operators, give description of such spectra of…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
This paper has been withdrawn by the authors. A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those…
We develop a systematic way for constructing bispectral algebras of commuting ordinary differential operators of any rank $N$. It combines and unifies the ideas of Duistermaat-Gr\"unbaum and Wilson. Our construction is completely…
We show the existence of fundamental solutions for p-adic pseudo-differential operators with polynomial symbols.
In this paper we discuss some results related to commuting ordinary differential operators of rank greater than one.
We identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space $\R$. For a general algebra of parametric pseudodifferential operators,…
Periodic integral operators over Cayley-Dickson algebras related with integration of PDE are studied. Their continuity and spectra are investigated.
We provide a brief survey of a certain algebra of operators on symmetric polynomials, and collect a number of previously known results in the field.