Introduction to the Theory of Singular Integral Operators with Shift

Softcover Nachdruck of the original 1. Auflage 1994
ISBN: 978-94-010-4515-5
Verlag: Springer Netherlands

Buch, Englisch, Band 289, 288 Seiten, Paperback, Format (B × H): 160 mm x 240 mm, Gewicht: 495 g

Reihe: Mathematics and Its Applications

problem (0. 2) was the same u that of problem (0. 1). Incidentally, later on Mandzhavidze and Khvedclidze (I) and Simonenko (I) achieved a direct reduction of problem (0. 2) to problem (0. 1) with the help of conformal mappings. Apparenlly, the first paper in which SIES were considered was the paper by Vekua (2) published in 1948. Vekua verified that the equation (0. 3) where (1; € C(f), 5 is the operator of 'ingular integration with a Cauchy kernel (Srp)(!) "" (". i)-I fr(T - t)-lrp(T)dT, W is the shift operator (WrpHt) = rp{a(t', in the case 01 = - (13,0, = 0., could be reduced to problem (0. 2). We note thai, in problem (0. 2), the shift ott) need not be a Carlemao shift,. ei., it is oot necessary that a. (t): t for some integer 11 ~ 2, where ai(l) "" o(ok_dt)), 0(1(1):!. For the first time, the condition 0,(1) == 1 appeared in BPAFS theory in connection with the study of the problem (0. 4) by Carle man (2) who, in particular, showed that problem (0. 4) Wall a natural generalization of the problem on the existence of an a. utomorphic function belonging to a certain group of Fucs. Thus, the paper by Vckua (2) is also the fint paper in which a singular integral equation with a non·Carieman 5hifl is on c sidered.

Zielgruppe

Research

Autoren/Hrsg.

Litvinchuk, Georgii S.

Kravchenko, Viktor G.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Integralrechnungen- und -gleichungen
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

1. Background information.- 2.Noetherity criterion and a formula for the index of a singular integral functional operator of first order in the continuous case.- 3. The Noether theory of a singular integral functional operator of finite order in the continuous case.- 4. The Noether theory of singular integral functional operators with continuous coefficients on a non-closed contour.- 5. The Noether theory in algebras of singular integral functional operators.- References.