A regular interpolation problem and its applications

The Abstract Interpolation Problem and Applications

A number of classical interpolation problems can be reduced to the following scheme. One is interested in the finding Schur class operator functions w(ζ) : E1 → E2, with ζ ∈ D, that satisfy certain interpolation conditions. The data of the problem are encoded in the Lyapunov identity D(T2x, T2y) − D(T1x, T1y) = 〈M1x, M1y〉 − 〈M2x, M2y〉, where x, y are elements of a vector space X, D is a positiv...

Relationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications

ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...

Regular Triangulation in 3D and Its Applications

A Generalized Turán Problem and its Applications

The investigation of conditions guaranteeing the appearance of cycles of certain lengths is one of the most well-studied topics in graph theory. In this paper we consider a problem of this type which asks, for fixed integers ` and k, how many copies of the k-cycle guarantee the appearance of an `-cycle? Extending previous results of Bollobás–Győri–Li and Alon–Shikhelman, we fully resolve this p...

A Basic Interpolation Problem

A basic interpolation problem, which includes bitangential matrix versions of a number of classical interpolation problems, is formulated and solved. Particular attention is placed on the development of the problem in a natural way and upon the fundamental role played by a special class of reproducing kernel Hilbert spaces of vector-valued meromorphic functions that originate in the work of L. ...