Related papers: Krein's strings whose spectral functions are of po…
On donne une condition necessaire et suffisante pour l'existence de modules de dimension finie sur l'algebre de Cherednik rationnelle associee a un systeme de racines.
It is shown that from two strings that are partially random and independent (in the sense of Kolmogorov complexity) it is possible to effectively construct polynomially many strings that are random and pairwise independent. If the two…
We get a generalization of Krein's formula -which relates the resolvents of different selfadjoint extensions of a differential operator with regular coefficients- to the non-regular case $A=-\partial_x^2+(\nu^2-1/4)/x^2+V(x)$, where…
Suppose that $f: \bR^n\to\bR^n$ is a mapping of $K$-bounded $p$-mean distortion for some $p>n-1$. We prove the equivalence of the following properties of $f$: doubling condition for $J(x,f)$ over big balls centered at origin, boundedness of…
We describe how spectral functions of differential operators appear in the quantum field theory context. We formulate consistency conditions which should be satisfied by the operators and by the boundary conditions. We review some modern…
We prove several results on the multiplier spectrum of polynomials. We provide a detailed proof of the theorem stating that the multiplier spectrum morphism is generically injective on the moduli space of polynomials. We obtain a…
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…
The paper is devoted to optimization of resonances for Krein strings with total mass and statical moment constraints. The problem is to design for a given $\alpha \in \R$ a string that has a resonance on the line $\alpha + \i \R$ with a…
Simple necessary and sufficient conditions for a $n$-tuple of noncommutative polynomials to be a cyclic gradient are given and similarly for a noncommutative polynomial to have a vanishing cyclic gradient. Connections with free probability…
In the present note a spectral theorem for normal definitizable linear operators on Krein spaces is derived by developing a functional calculus $\phi \mapsto \phi(N)$ which is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the…
In string theory, the consequences of replacing the measure of integration $\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is a density built out of degrees of freedom independent of the metric $\gamma_{ab}$…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
The question of when two skew Young diagrams produce the same skew Schur function has been well-studied. We investigate the same question in the case of stable Grothendieck polynomials, which are the K-theoretic analogues of the Schur…
We prove a necessary condition for some polynomials of Kasami degree to be APN over F_{q^n} for large n.
The orthogonality relations of multivariate Krawtchouk polynomials are discussed. In case of two variables, the necessary and sufficient conditions of orthogonality is given by Gr\"unbaum and Rahman in [SIGMA 6 (2010), 090, 12 pages,…
In this paper, we give a description of the self-injective dimension of string algebras and obtain a necessary and sufficient condition for a string algebra to be Gorenstein.
For an infinite penny graph, we study the finite-dimensional property for the space of harmonic functions, or ancient solutions of the heat equation, of polynomial growth. We prove the asymptotically sharp dimensional estimate for the above…
Let $A$ be a matrix of size $n \times n$ over an algebraically closed field $F$ and $q(t)$ a monic polynomial of degree $n$. In this article, we describe the necessary and sufficient conditions of $q(t)$ so that there exists a rank one…
The main result of the paper is a description of the class of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. We prove that this class of functions…
In this paper we prove that any Artin--Schreier extension of a congruence rational function field is contained in the composite of a cyclotomic function field and a constant field extension that are explicitly prescribed.