Abstract
Integral geometry problems of Volterra type are problems which can be represented as problems of solution of Volterra operator equations. Here we consider two integral geometry problems in which integration is carried out along parts of parabolas. In contrast to the most of investigated integral geometry problems of Volterra type, for the problems concerned there take place exponential estimates of conditional stability, i. e., these problems are weakly ill-posed. The results presented in this paper were obtained by the author together with Akr. Kh. Begmatov (Samarkand State University).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Romanov, V.G.:Some Inverse Problems for Equations of Hyperbolic TypeNauka, Novosibirsk, 1972 (in Russian).
Samko, S.G., Kilbas, A.A., and Marichev, O.I.:Integrals and Derivatives of Fractional Order and Some Their ApplicationsNauka i Tekhnika, Minsk, 1973 (in Russian).
Nikol’skii, S.M.:Approximation of Functions of Many Variables and Embedding TheoremsNauka, Moscow, 1969 (in Russian).
Kamke, E.:Reference Book on Ordinary Differential EquationsNauka, Moscow, 1976 (in Russian).
Gradshtein, I.S. and Ryzhik, I.M.:Tables of Integrals, Sums, Series, and ProductsFizmatgiz, Moscow, 1962 (in Russian).
Lavrent’ev, M.A. and Shabat, B.V.:Methods of the Theory of Functions of Complex VariableNauka, Moscow, 1986 (in Russian).
Evgrafov, M.A.:Asymptotic Estimates and Entire FunctionsNauka, Moscow, 1979 (in Russian).
Lavrent’ev, M.M.:Integral geometry and inverse problems, in Ill-Posed Problems of Mathematical Physics and CalculusNauka, Novosibirsk, 1984, pp. 81–86 (in Russian).
Krein, S.G.:Linear Differential Equations in a Banach SpaceNauka, Moscow, 1967 (in Russian).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Lavrent’ev, M.M. (2000). Two Integral Geometry Problems of Volterra Type on a Plane. In: Spigler, R. (eds) Applied and Industrial Mathematics, Venice—2, 1998. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4193-2_7
Download citation
DOI: https://doi.org/10.1007/978-94-011-4193-2_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5823-0
Online ISBN: 978-94-011-4193-2
eBook Packages: Springer Book Archive