Traces and Determinants of Linear Operators

ISBN-13: 9783764361778 / Angielski / Twarda / 2000 / 267 str.

Prof. Israel Gohberg;Seymour Goldberg;Naum Krupnik

Opis

All the important classical examples of traces and determinants sugges, Ruston and Grothendieck are exhibited. In particular, the determinants which were first introduced in their investigations of infinite systems of li near equations stemmingfrom problems in celestial mechanics are studie d. Most of FredholmFs seminal results are presented in this book by th e editorsf own means. Formulas for traces and determinants in a Hilber t space setting are readily derived, again. Also investigated are gene ralizations to Banach spaces. Furthermore, a large part of this book i s devoted to generalizations of the regularized determinants introduce d by Hilbert and Carleman, and regularized determinants of higher orde r in embedded algebras are introduced. Much attention is paid to integ ral operators with semi-separable kernels, and explicit formulas of tr aces and determinants are given.