Related papers: The Grunsky operator and quasiconformality: old an…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
Many mechanical systems have configuration spaces that admit symmetries. Mathematically, such symmetries are modelled by the action of a group on a topological space. Several variations of topological complexity have emerged that take…
In this paper, we build on our previous work to further investigate the role of evanescent operators in gauge theories, with a particular focus on their contribution to violations of unitarity. We develop an efficient method for calculating…
The Minkowski function is a crucial tool used in the study of balanced domains and, more generally, quasi-balanced domains in several complex variables. If a quasi-balanced domain is bounded and pseudoconvex then it is well-known that its…
Let $V$ be a rational, selfdual, $C_2$-cofinite vertex operator algebra of CFT type, and $G$ a finite automorphism group of $V.$ It is proved that the kernel of the representation of the modular group on twisted conformal blocks associated…
We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…
We design a quasi-interpolation operator from the Sobolev space $H^1_0(\Omega)$ to its finite-dimensional finite element subspace formed by piecewise polynomials on a simplicial mesh with a computable approximation constant. The operator 1)…
A collection of infinite dimensional complete vector fields $\left\{V_i\right\}_{i=1}^{\infty}$ acting on a locally convex manifolds $M$ on which a smooth positive measure $\mu$ is defined was considered. It was assumed that the vector…
The main results of this paper show that various coarse (`large scale') geometric properties are closely related. In particular, we show that property A implies the operator norm localisation property, and thus that norms of operators…
The core of quantum tomography is the possibility of writing a generally unbounded complex operator in form of an expansion over operators that are generally nonlinear functions of a generally continuous set of spectral densities--the…
If we add a simple rotation term to both the Ornstein-Uhlenbeck semigroup and the definition of the H-derivative, then analogue to the classical Malliavin calculus on the real Wiener space [I. Shigekawa, Stochastic analysis, 2004], we get a…
In this short note we prove an equivariant version of the formality of multidiffirential operators for a proper Lie group action. More precisely, we show that the equivariant Hochschild-Kostant-Rosenberg quasi-isomorphism between the…
Convergence of operators acting on a given Hilbert space is an old and well studied topic in operator theory. The idea of introducing a related notion for operators acting on arying spaces is natural. However, it seems that the first…
Quasiconformal homeomorphisms of the whole space Rn, onto itself normalized at one or two points are studied. In particular, the stability theory, the case when the maximal dilatation tends to 1, is in the focus. Our main result provides a…
We develop techniques for computing superconformal blocks in 4d superconformal field theories. First we study the super-Casimir differential equation, deriving simple new expressions for superconformal blocks for 4-point functions…
It is proved that given a divergence operator on the structural sheaf of graded commutative algebras of a supermanifold, it is possible to construct a generating operator for the Krashil'shchik-Schouten bracket. This is a particular case of…
In the preceding paper [arXiv:hep-th/0604217], we construct the Dirac operator and the integral on the canonical noncommutative space. As a matter of fact, they are ones on the noncommutative torus. In the present article, we introduce the…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
This review article intends to introduce the reader to non-integrable geometric structures on Riemannian manifolds and invariant metric connections with torsion, and to discuss recent aspects of mathematical physics--in particular…
Group equivariant operators are playing a more and more relevant role in machine learning and topological data analysis. In this paper we present some new results concerning the construction of $G$-equivariant non-expansive operators…