Related papers: A sufficient condition for a Rational Differential…

Given an irreducible local conformal net A of von Neumann algebras on the circle and a finite-index conformal subnet B of A, we show that A is completely rational iff B is completely rational. In particular this extends a result of F. Xu…

We give a formula for the determinant of an $n\times n$ matrix with entries from a commutative ring with unit. The formula can be evaluated by a "straight-line program" performing only additions, subtractions and multiplications of ring…

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily…

For Fr{\'e}chet spaces E and F we write (E,F) \in {B} if every continuous linear operator from E to F is bounded. Let l be a Banach sequence space with a monotone norm in which the canonical system (e_{n}) is an unconditional basis. We…

We consider differential operators $L$ acting on functions on a Riemannian surface, $\Sigma$, of the form $$L = \Delta + V -a K ,$$where $\Delta$ is the Laplacian of $\Sigma$, $K$ is the Gaussian curvature, $a$ is a positive constant and $V…

The purpose of this article is to develop an algebraic approach to the problem of integrable classification of differential-difference equations with one continuous and two discrete variables. As a classification criterion, we put forward…

We study the eigenfunctions of the classical Liouville operator and investigate the conditions they must obey to be separable as a product state. We point out that the conditions for separability are equivalent to requirements of…

We show that for an entire function $\varphi$ belonging to the Fock space ${\mathscr F}^2(\mathbb{C}^n)$ on the complex Euclidean space $\mathbb{C}^n$, the integral operator \begin{eqnarray*} S_{\varphi}F(z)=\int_{\mathbb{C}^n} F(w) e^{z…

Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…

The work is devoted to constructing a wide class of differential-functional dynamical systems, whose rich algebraic structure makes their integrability analytically effective. In particular, there is analyzed in detail the operator Lax type…

The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on $^*$-algebras. We describe the extreme points of order intervals, and give a nontrivial sufficient…

A new class of infinite-dimensional Lie algebras given a name of Lax operator algebras, and the related unifying approach to finite-dimensional integrable systems with spectral parameter on a Riemann surface, such as Calogero--Moser and…

For an $n$-qubit system, a rational function on the space of mixed states which is invariant with respect to the action of the group of local symmetries may be viewed as a detailed measure of entanglement. We show that the field of all such…

Consider a_1,a_2,...,a_n, arbitrary elements of R. We characterize those real functions f that decompose into the sum of a_j-periodic functions, i.e., f=f_1+...+f_n with D_{a_j}f(x):=f(x+a_j)-f(x)=0. We show that f has such a decomposition…

We consider a class of nonlinear non-diagonal elliptic systems with $p$-growth and establish the $L^q$-integrability for all $q\in [p,p+2]$ of any weak solution provided the corresponding right hand side belongs to the corresponding…

Given a random sequence of holomorphic maps $f_1,f_2,f_3,...$ of the unit disk $\Delta$ to a subdomain $X$, we consider the compositions $$F_n=f_1 \circ f_{2} \circ ... f_{n-1} \circ f_n.$$ The sequence $\{F_n\}$ is called the {\em iterated…

We introduce the linear operators of fractional integration and fractional differentiation in the framework of the Riemann-Liouville fractional calculus. Particular attention is devoted to the technique of Laplace transforms for treating…

Let $\Lambda$ be a $\mathbb{Z}$-graded artin algebra. Two classical results of Gordon and Green state that if $\Lambda$ has only finitely many indecomposable gradable modules, up to isomorphism, then $\Lambda$ has finite representation…

Let $A$ be an operator on {a separable } Hilbert space $\cH$, and let $G \subset \cH$. It is known that - under appropriate conditions on $A$ and $G$ - the set of iterations $F_G(A)= \{A^j \gbf \; | \; \gbf \in G, \; 0 \leq j \leq L(\gbf)…

We consider linear spectral-meromorphic (s-meromorphic) OD operators at the real axis such that all local solutions to the eigenvalue problems are meromorphic for all $\lambda$. By definition, rank one algebro-geometrical operator $L$ admit…