This collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C^*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

Readership

Graduate students and research mathematicians.

Table of Contents

• T. Ya. Azizov, N. D. Kopachevskii, and L. D. Orlova -- Evolution and spectral problems related to small motions of viscoelastic fluid
• A. B. Antonevich and A. V. Lebedev -- Functional equations and functional operator equations. A $C^*$-algebraic approach
• M. V. Bondarko and S. V. Vostokov -- Isomorphism of ideals regarded as Galois modules of complete discrete valuation fields with residue field of positive characteristic
• I. V. Kamotskii and S. A. Nazarov -- Spectral problems in singularly perturbed domains and selfadjoint extensions of differential operators
• V. A. Sloushch -- Discrete spectrum in gaps of the spectrum under strong perturbations of fixed sign
• N. D. Filonov -- On bounded solutions to the equation div $u = f$ in a plane domain
• B. Ya. Shteinberg -- Compactification of a locally compact group and the Noethericity of convolution operators with coefficients on quotient groups
• N. S. Ermolaeva -- Prehistory of seminars at the St. Petersburg/Petrograd/Leningrad University