Introduction to the Theory of Singular Integral Operators with Shift (Hardcover, 1994 ed.)

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.

General

Imprint:	Springer
Country of origin:	Netherlands
Series:	Mathematics and Its Applications, 289
Release date:	May 1994
First published:	1994
Authors:	Viktor G. Kravchenko • Georgii S. Litvinchuk
Dimensions:	235 x 155 x 19mm (L x W x T)
Format:	Hardcover
Pages:	288
Edition:	1994 ed.
ISBN-13:	978-0-7923-2864-3
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
LSN:	0-7923-2864-7
Barcode:	9780792328643

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