Localization algorithms for singularities of solutions to convolution equations of the first kind / Ageev A. L.,Antonova T. V. // JOURNAL OF INVERSE AND ILL-POSED PROBLEMS. - 2008. - V. 16, l. 7. - P. 639-650.

ISSN/EISSN:

0928-0219 / нет данных

Type:

Article

Abstract:

In this paper we construct and investigate localization algorithms for isolated singularities of a function which is a solution to a linear convolution equation of the first kind whose right-hand side is given with an error. We consider two types of singularities: delta-functions and discontinuities of the first kind. A problem for singularities localization is an ill-posed problem having perturbation. We use averaging methods defined by an averaging functional to obtain the singularities. We formulate conditions that the averaging functional must satisfy. For convolution equations, using the Fourier transform, we obtained upper estimates of precision of the singularities localization, separation threshold and other important characteristics of the supposed methods.

Author keywords:

SPECTRAL INSTRUMENTS; RESOLVING POWER

DOI:

10.1515/JIIP.2008.039

Web of Science ID:

ISI:000263793500001

Соавторы в МНС:

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Другие поля

Поле	Значение
Month	NOV
Publisher	WALTER DE GRUYTER \& CO
Address	GENTHINER STRASSE 13, D-10785 BERLIN, GERMANY
Language	English
Keywords-Plus	SPECTRAL INSTRUMENTS; RESOLVING POWER
Research-Areas	Mathematics
Web-of-Science-Categories	Mathematics, Applied; Mathematics
Author-Email	ageev@imm.uran.ru tvantonova@imm.uran.ru
Funding-Acknowledgement	RFBR {[}06-01-00116]
Funding-Text	supported by RFBR (grant No. 06-01-00116)
Number-of-Cited-References	24
Journal-ISO	J. Inverse Ill-Posed Probl.
Doc-Delivery-Number	413LB