This self-contained introduction to the behavior of several spectral characteristics of large Toeplitz band matrices is the first systematic presentation of a relatively large body of knowledge, covering everything from classic results to the most recent developments. The spectral characteristics include determinants, eigenvalues and eigenvectors, pseudospectra and pseudomodes, singular values, norms, and condition numbers. Toeplitz matrices emerge in many applications and the literature on them is immense. They remain an active field of research with many facets, and the material on banded...

(jointly with V.P. Zakharyuta and V.I. Yudovich), including a calculation of the capacity of condensers of complex form and dielectric materials with complex structure. In 1967, at the age of 32, six years after he defended his Ph.D. thesis, I.B. - monenko defended his thesis for a degree of Doctor of Science. In this thesis, entitled "Operators of local type and some other problems of the theory of linear operators," he sharply turned towards the wide usage of the general methods of functional analysis. In 1971 professor I.B. Simonenko became the head of the - merical Mathematics Chair. The...

We offer the reader of this book some specimens of "infinity" that we seized from the "mathematical jungle" and trapped within the solid cage of analysis The creation of the theory of singular integral equations in the mid 20th century is associated with the names of N.1. Muskhelishvili, F.D. Gakhov, N.P. Vekua and their numerous students and followers and is marked by the fact that it relied principally on methods of complex analysis. In the early 1960s, the development of this theory received a powerful impulse from the ideas and methods of functional analysis that were then brought into...