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On sharpness, applications and generalizations of some Carleman type inequalities
Department of Numerical Methods and Analysis, Technical University, Sofia, Bulgaria.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
1996 (English)In: Tohoku mathematical journal, ISSN 0040-8735, Vol. 48, no 1, p. 1-22Article in journal (Refereed) Published
Abstract [en]

Carleman’s inequality for Hilbert-Schmidt operators and its generalizations for Schatten-von Neumann operator ideals (see [7]) are shown to be sharp in a certain sense. Explicit classes of extremizing operators are found on which the generalized Carleman inequalities turn to asymptotic equalities. Applications are made to a priori estimation of the solutions of Fredholm and Volterra first- and second kind integral equations and to perturbation and error analysis. Some further generalizations are considered which extend the applications to singular integral equations, pseudodifferential equations and analytic functions of operator argument.

Place, publisher, year, edition, pages
1996. Vol. 48, no 1, p. 1-22
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-2469DOI: 10.2748/tmj/1178225409ISI: A1996UB58900001Scopus ID: 2-s2.0-0030304676Local ID: 017b3ab0-b600-11db-bf94-000ea68e967bOAI: oai:DiVA.org:ltu-2469DiVA, id: diva2:975321
Note

Godkänd; 1996; 20070206 (kani)

Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2022-05-04Bibliographically approved

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Persson, Lars-Erik

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