Nahum Krupnik

Influence of some B. V. Khvedelidze's Results on the Development of Fredholm Theory for SIOs

abstract:
A concise survey on the construction of the spectra, symbols and index-formulas for singular integral operators with piecewise continuous coefficients in the spaces $L_p^n(\Gamma,\rho)$ is given. Influence of some results by B. V. Khvedelidze on this research is shown. Several interesting associated results, obtained during this research, and their applications are discussed in appendix. An open question is stated. Some historical information, related to this paper is presented in the introduction.

Mathematics Subject Classification: Primary 45E10, 45E05, 47B48; Secondary 47B35

Key words and phrases: Banach algebras, Fredholm theory, spectrum, symbol, index