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We study the behaviour of functions of pairs of commuting self-adjoint operators under perturbations by relatively bounded operators. We obtain analogs of our earlier results for functions of a single self-adjoint operator under relatively…
In this article, we describe the spectral sheaves of algebras of commuting differential operators of genus one and rank two with singular spectral curve, solving a problem posed by Previato and Wilson. We also classify all indecomposable…
In this paper we study self-adjoint commuting ordinary differential operators. We find sufficient conditions when an operator of fourth order commuting with an operator of order $4g+2$ is self-adjoint. We introduce an equation on…
We consider a family of integral operators which appears when analyzing layered equilibria and front dynamics of a phase kinetics equation with a conservation law. We study the spectra of these operators in $L^2$ and derive a lower bound…
In this paper we establish hypercyclicity of continuous linear operators on $H(\mathbb{C})$ that satisfy certain commutation relations.
We associate to an integral operator a discrete one which is conceptually simpler, and study the relations between them.
The isomorphism between the reduction algebra and the invariant differential operators on G/H is sketched.
We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating and synchronising groups can be described via properties of…
The various formulations of scattering amplitudes presented in recent years have underlined a hidden unity among very different theories. The KLT and BCJ relations, together with the CHY formulation, connect the S-matrices of a wide range…
We obtain a family of functional identities satisfied by vector-valued functions of two variables and their geometric inversions. For this we introduce particular differential operators of arbitrary order attached to Gegenbauer polynomials.…
Symmetry is present in many tasks in computer vision, where the same class of objects can appear transformed, e.g. rotated due to different camera orientations, or scaled due to perspective. The knowledge of such symmetries in data coupled…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at $0$, known to hold for bounded scalar type spectral…
We derive the most general families of differential operators of first and second degree semi-commuting with the differential operators of the Heun class. Among these families we classify all those families commuting with the Heun class. In…
Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary…
In this article we consider a class of integrable operators and investigate its connections with the following theories:the spectral theory of non-self-adjoint operators, the Riemann-Hilbert problem, the canonical differential systems and…
Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…
The space of entire functions which are integrable with respect to the Gaussian weight, known also as the Fock space, is one of the preferred functional Hilbert spaces for modelling and experimenting harmonic analysis, quantum mechanics or…
In this paper we study the commutators of fractional type integral operators. This operators are given by kernels of theform $$K(x,y)=k_1(x-A_1y)k_2(x-A_2y)\dots k_m(x-A_my),$$ where $A_i$ are invertibles matrices and each $k_i$ satisfies a…