Related papers: Krein's strings whose spectral functions are of po…
We consider polynomials which take integer values on the integers (IVPs), and satisfy an additional growth condition on the natural numbers. Elkies and Speyer, answering a question by Dimitrov, showed there is a critical exponential growth…
The Krein transform is the real counterpart of the Cayley transform and gives a one-to-one correspondence between the positive relations and symmetric contractions. It is treated with a slight variation of the usual one, resulting in an…
Based on continuity properties of the de Branges correspondence, we develop a new approach to study the high-energy behavior of Weyl-Titchmarsh and spectral functions of $2\times2$ first order canonical systems. Our results improve several…
This paper solves the integral equation which describes the oscillating inhomogeneous string, by using a spectral expansion method in terms of Chebyshev polynomials. The result is compared with the solution of the corresponding differential…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
We derive the necessary and sufficient condition, for a given Polynomial Recurrence Sequence to converge to a given target rational K. By converge, we mean that the Nth term of the sequence, is equal to K, as N tends to positive infinity.…
We present a number of relations involving the number of cliques in a graph and its spectral radius.
We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We…
In string theory various projections have to be imposed to ensure supersymmetry. We study the consequences of these projections in the presence of world sheet boundaries. A-type boundary conditions come in several classes; only boundary…
We provide new necessary and sufficient conditons for ensuring strong quasiconvexity in the nonsmooth case and, as a consequence, we provide a proof for the differentiable case. Furthermore, we improve the quadratic growth property for…
The paper studies the question of existence of polynomials with given roots over associative non-commutative rings with identity. It is shown that in the case of an associative division ring for arbitrary n elements of this ring there…
Necessary and sufficient conditions under which two real functions defined on the real interval can be separated by a polynomial are given. An immediate consequence of the main result is the existence of the polynomial separation of convex…
We compute spectra of particles produced during a dilaton-driven kinetic inflation phase within string cosmology models. The resulting spectra depend on the parameters of the model and on the type of particle and are quite varied, some…
Necessary and sufficient conditions for Lipschitzness of the Lempert and Green functions are found in terms of their boundary behaviors.
We study the polyregular string-to-string functions, which are certain functions of polynomial output size that can be described using automata and logic. We describe a system of combinators that generates exactly these functions. Unlike…
In the critical bosonic string theory, we explicitly evaluate the three point scattering amplitude at tree level, of a photon with two massive higher spins. The massive excitations belong to states of the form $A_{-r_1}^{s_1}…
We show that solutions to Krein systems, the continuous frequency analogue of orthogonal polynomials on the unit circle, generated by an $A_2 (\mathbb{R})$ weight $w$ satisfying $w-1 \in L^1 (\mathbb{R}) + L^2 (\mathbb{R})$, are uniformly…
We show that the joint spectral radius is pointwise H\"older continuous. In addition, the joint spectral radius is locally H\"older continuous for $\varepsilon$-inflations. In the two-dimensional case, local H\"older continuity holds on the…
A description of the Ziegler spectrum is given for trivial extensions of tubular algebras and related self-injective algebras of tubular type.
In this paper, we start by showing that the intertwining relationship between two minimal Markov semigroups acting on Hilbert spaces implies that any recurrent extensions, in the sense of It\^o, of these semigroups satisfy the same…