Convolution equations and singular integral operators

Viac o knihe

This book presents English translations of several influential papers on discrete and continuous convolution operators and singular integral operators originally published in Russian over thirty years ago. Despite their age, these works have proven to be significant in both pure and applied mathematics and engineering. The book is divided into two parts. The first part includes five papers by I. Gohberg and G. Heinig, focusing on the inversion of finite block Toeplitz matrices and their continuous counterparts, addressing both direct and inverse problems, as well as the theory of discrete and continuous resultants. The second part features eight papers by I. Gohberg and N. Krupnik, which explore one-dimensional singular integral operators with discontinuous coefficients across various spaces. Key topics include localization theory, the structure of the symbol, and equations with shifts. This compilation offers English-speaking readers a unique chance to engage with foundational work on Toeplitz matrices and singular integral operators, which are now regarded as classical. The translator and editors have corrected several misprints and minor inaccuracies during the preparation of the book, and special thanks are extended to A. Karlovich for his meticulous translation. This work serves as a tribute to the late Israel Gohberg, a remarkable mathematician.