Related papers: Finite Gap Jacobi Matrices: A Review
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We study spaces of reflectionless Jacobi matrices. The main theme is the following type of question: Given a reflectionless Jacobi matrix, is it possible to approximate it by other reflectionless and, typically, simpler Jacobi matrices of a…
Family of replica matrices, related to general ultrametric spaces, is introduced. These matrices generalize the known Parisi matrices. Some functionals of replica approach are computed.
From the literature it is known that orthogonal polynomials as the Jacobi polynomials can be expressed by hypergeometric series. In this paper, the authors derive several contiguous relations for terminating multivariate hypergeometric…
In this paper we investigate congruence relationships of particular finite generalized harmonic numbers sums. We suggest more transparent and simpler method to analyse these sums and present several additional results for certain special…
We study bounds on eigenvalue gaps for finite quotients of periodic Jacobi matrices on trees. We prove an Alon-Boppana type bound for the spectral gap and a comparison result for other eigenvalue gaps.
We define Jacobi forms of indefinite lattice index, and show that they are isomorphic to vector-valued modular forms also in this setting. We also consider several operations of the two types of objects, and obtain an interesting bilinear…
In this note we discuss Morita equivalence classes of arbitrary finitely presented algebras
We analyze the relationship between the covering of the Jacobi group and the squeezed states. We attach some nonclassical states to the Jacobi group. The matrix elements of the Jacobi group are presented.
Highlights of Quark Matter 95 are discussed.
In this note, finite type epimorphisms of rings are characterized.
We review old and new properties of Hopf manifolds from the point of view of their analytic and metric structure.
We define recurrence matrices and study a few properties (links with automatic sequences, branch groups etc.) of them.
Symmetric Jacobi matrices on one sided homogeneous trees are studied. Essential selfadjointness of these matrices turns out to depend on the structure of the tree. If a tree has one end and infinitely many origin points the matrix is always…
This paper provides a finite pair of biorthogonal matrix polynomials and their finite biorthogonality, several recurrence relations, matrix differential equation, generating function and integral representation.
This note presents a summary and review of various conditions and characterizations for matrix stability (in particular diagonal matrix stability) and matrix stabilizability.
We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well known gap in the spectrum of the Laplacian on the upper half-plane with hyperbolic metric. We make some…
An introduction and overview of constructive reverse mathematics.
Let $\fre\subset\bbR$ be a finite union of $\ell+1$ disjoint closed intervals and denote by $\omega_j$ the harmonic measure of the $j$ leftmost bands. The frequency module for $\fre$ is the set of all integral combinations of $\omega_1,...,…
We study contact resolutions of Jacobi structures which are contact on an open subset. We give several classes of examples, as well as classes for which it cannot exist.