Two-term Equations (A + QB)ϕ = f with an Involutive Operator Q; an Abstract Approach and Applications

Nikolai Karapetiants and Stefan Samko
Additional contact information
Nikolai Karapetiants: Rostov State University, Department of Mathematics
Stefan Samko: Universidade do Algarve, Faculdade de Ciências e Tecnologia

Chapter 4 in Equations with Involutive Operators, 2001, pp 153-222 from Springer

Abstract: Abstract In Sections 11–12 we presented an approach to the investigation of Fredholmness of singular integral equations with Carleman shift on a closed or open curve in the case of continuous coefficients. This approach is also applicable to many other types of equations, because it, in fact, gives some general scheme of the investigation of Fredholmness of operators, containing an involutive operator Q, that is, an operator such that Q 2 = I, or, more generally, Q n = I. This approach may be applicable, in particular, to a) convolution equations with reflection; b) discrete convolutions with oscillating coefficients; c) singular integral equations with Carleman shift on the axis R1, when the shift function is unbounded; d) singular integral equations with Carleman shift in the case of piecewise continuous coefficients, etc.

Keywords: Compact Operator; Singular Integral Equation; Singular Integral Operator; Fredholm Operator; Abstract Equation (search for similar items in EconPapers)
Date: 2001
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0183-0_4

Ordering information: This item can be ordered from
http://www.springer.com/9781461201830

DOI: 10.1007/978-1-4612-0183-0_4

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().