|
|
Автор: Jesse Russell
Год: 2013
Издание:
Книга по Требованию
Страниц: 108
ISBN: 9785508949853
High Quality Content by WIKIPEDIA articles! In mathematics, singular integral operators on closed curves arise in problems in analysis, in particular complex analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth Jordan curve in the complex plane and are related by a simple algebraic formula. The Hilbert transform is an involution and the Cauchy transform an idempotent. The range of the Cauchy transform is the Hardy space of the bounded region enclosed by the Jordan curve. The theory for the original curve can be deduced from that on the unit circle, where, because of rotational symmetry, both operators are classical singular integral operators of convolution type. The Hilbert transform satisfies the jump relations of Plemelj and Sokhotski, which express the original function as the difference between the boundary values of holomorphic functions on the region and its complement. Singular...
|
|
Jesse RussellSingular integral operators on closed curves
Christ M.Lectures on Singular Integral Operators
W.KoppelmanPerturbation of continuious spectra and singular integral operators