Related papers: Representation Theorems for indefinite quadratic f…

We give formulas for the number of representations of non negative integers by various quadratic forms. We also give evaluations in the case of sum of two cubes (cubic case) and the quintic case, as well. We introduce a class of generalized…

The representation theorem is obtained for functionals of non-Markov processes and their first exit times from bounded domains. These functionals are represented via solutions of backward parabolic Ito equations. As an example of…

An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…

We show that kernel-based quadrature rules for computing integrals can be seen as a special case of random feature expansions for positive definite kernels, for a particular decomposition that always exists for such kernels. We provide a…

The tensor and exterior squares of a completely continuous non-negative linear operator $A$ acting in the ideal space $X(\Omega)$ are studied. The theorem representing the point spectrum (except, probably, zero) of the tensor square $A…

In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth…

We extend inner fluctuations to spectral triples that do not fulfill the first-order condition. This involves the addition of a quadratic term to the usual linear terms. We find a semi-group of inner fluctuations, which only depends on the…

Representation theory of an infinite dimensional Galilean conformal algebra introduced by Martelli and Tachikawa is developed. We focus on the algebra defined in (2+1) dimensional spacetime and consider central extension. It is then shown…

This paper presents analogous results of Hua [7][8] on numbers of representations of quivers over finite fields which respect nilpotent relations under certain assumptions. A closed formula which counts isomorphism classes of absolutely…

For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…

In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…

In this lecture, we survey a number of recent results and developments regarding the representation theory of infinite-dimensional quantum groups (quantum affine algebras and related algebras), as well as their connections with cluster…

We give some extensions of Mercer's theorem to continuous Carleman kernels inducing unbounded integral operators.

The representation theory (idempotents, quivers, Cartan invariants and Loewy series) of the higher order unital peak algebras is investigated. On the way, we obtain new interpretations and generating functions for the idempotents of descent…

Inverse spectral problems are studied for the second order integro-differential operators on a finite interval. Properties of spectral characteristic are established, and the uniqueness theorem is proved for this class of inverse problems.

Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…

This article is a continuation of arXiv:2401.14977. We study the concentration properties of spectral projectors on manifolds, in connection with the uncertainty principle. In arXiv:2401.14977, the second author proved an optimal…

A number field $k$ admits a binary integral quadratic form which represents all integers locally but not globally if and only if the class number of $k$ is bigger than one. In this case, there are only finitely many classes of such binary…

Adapting the method of Andrews-Clutterbuck we prove an eigenvalue gap theorem for a class of non symmetric second order linear elliptic operators on a convex domain in euclidean space. The class of operators includes the Bakry-Emery…

We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…