×

Class of problems of integral geometry on the plane. (English. Russian original) Zbl 0698.53042

Sib. Math. J. 30, No. 4, 549-554 (1989); translation from Sib. Mat. Zh. 30, No. 4(176), 62-68 (1989).
The problem referred to in the title is a perturbation of the problem of determining a function from the values of its line integrals along parabolas of the form \((x_ 0+h, y_ 0-h^ 2).\) For this strongly ill- posed problem, the author proves a uniqueness theorem, generalizing a result of V. G. Romanov [Sib. Mat. Zh. 8, 1206-1208 (1967 Zbl 0156.359)].
Reviewer: M.Katz

MSC:

53C65 Integral geometry

Citations:

Zbl 0156.359
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] M. M. Lavrent’ev and A. L. Bukhgeim, ?A class of operator equations of the first kind,? Funkts. Anal. Prilozhen.,7, No. 4, 44-53 (1973).
[2] R. G. Mukhometov, ?A problem of integral geometry,? Mat. Probl. Geofiz.,6, No. 2, 212-245 (1975). · Zbl 0371.53051
[3] V. G. Romanov, ?Reconstruction of a function in terms of integrals over a family of curves,? Sib. Mat. Zh.,8, No. 5, 1206-1208 (1967).
[4] V. G. Romanov, ?A problem of integral geometry and the linearized inverse problem for a differential equation,? Sib. Mat. Zh.,10, No. 6, 1364-1374 (1969). · Zbl 0194.41404
[5] A. L. Bukhgeim, ?Carleman estimates for Volterra operators and the uniqueness of inverse problems,? in: Nonclassical Problems of Mathematical Physics [in Russian], Vychisl. Tsentr. Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1981), pp. 56-64.
[6] Yu. E. Anikonov, ?Quasimonotone operators,? Mat. Probl. Geofiz.,3, 86-99 (1972).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.