Related papers: Reduced transfer operators for singular difference…

The intertwining operator technique is applied to difference Schroedinger equations with operator-valued coefficients. It is shown that these equations appear naturally when a discrete basis is used for solving a multichannel Schroedinger…

We describe the spectral properties of the Jacobi operator $(Hy)_n= a_{n-1} y_{n-1}+a_{n}y_{n+1}+b_ny_n,$ $n\in\Z,$ with $a_n=a_n^0+ u_n,$ $b_n= b_n^0+ v_n,$ where sequences $a_n^0>0,$ $b_n^0\in\R$ are periodic with period $q$, and…

Let $M$ be a real hypersurface in complex projective space. The almost contact metric structure on $M$ allows us to consider, for any nonnull real number $k$, the corresponding $k$-th generalized Tanaka-Webster connection on $M$ and,…

The discrete spectrum of complex Jacobi matrices that are compact perturbations of the discrete laplacian is under consideration. The rate of stabilization for the the matrix entries which provides finiteness of the discrete spectrum and is…

This paper discusses operators lowering or raising the degree but preserving the parameters of special orthogonal polynomials. Results for one-variable classical (q-)orthogonal polynomials are surveyed. For Jacobi polynomials associated…

The paper studies the global convergence of the block Jacobi me\-thod for symmetric matrices. Given a symmetric matrix $A$ of order $n$, the method generates a sequence of matrices by the rule $A^{(k+1)}=U_k^TA^{(k)}U_k$, $k\geq0$, where…

Using the tool of unitary transformations of the extended receiver we perform simple operations with the non-diagonal elements of the initial sender's density matrix after their transferring to the receiver. These operations are following:…

We consider ergodic Jacobi operators and obtain estimates on the Lebesgue measure and the distance between maximum and minimum points of the spectrum in terms of the Lyapunov exponent. Our proofs are based on results from logarithmic…

This paper introduces a notion of gradient and an infimal-convolution operator that extend properties of solutions of Hamilton Jacobi equations to more general spaces, in particular to graphs. As a main application, the hypercontractivity…

It is established that the existence of non-isotropic vector field which Jacobi operator of maximal rank is an obstacle for the existence of non-trivial second-order symmetric parallel tensor field. In turns out that presence of such…

The convergence rate of a multigrid method depends on the properties of the smoother and the so-called grid transfer operator. In this paper we define and analyze new grid transfer operators with a generic cutting size which are applicable…

The little q-Jacobi function transform depends on three parameters. An explicit expression as a sum of two very-well-poised 8W7-series is derived for the dual transmutation kernel (a kind of non-symmetric Poisson kernel) relating little…

We study the inverse of the divergence operator on a domain $\Omega \subset R^3$ perforated by a system of tiny holes. We show that such inverse can be constructed on the Lebesgue space $L^p(\Omega)$ for any $1< p < 3$, with a norm…

In earlier work, Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the…

Space-time multivectors in Clifford algebra (space-time algebra) and their application to nonlinear electrodynamics are considered. Functional product and infinitesimal operators for translation and rotation groups are introduced, where…

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…

We construct noncomplete orthogonal systems on the ray $[0,\infty)$ that look like Jacobi polynomials $P_n(x)$ after a shift of degree $n\mapsto n+a$, where $a$ is a real constant. These systems are solutions of some exotic Sturm-Liouville…

We find all spectral type differential equations satisfied by the symmetric generalized ultraspherical polynomials which are orthogonal on the interval [-1,1] with respect to the classical symmetric weight function for the Jacobi…

This paper proposes an operator-theoretic framework that recasts the minimal value function of a nonlinear optimal control problem as an abstract bilinear form on a suitable function space. The resulting bilinear form is shown to satisfy an…

In this paper we provide new examples of geometrically trivial strongly minimal differential algebraic varieties living on nonisotrivial curves over differentially closed fields of characteristic zero. Our technique involves developing a…