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Integral geometry problems with perturbation on the plane. (English. Russian original) Zbl 0874.53054

Sib. Math. J. 37, No. 4, 747-752 (1996); translation from Sib. Mat. Zh. 37, No. 4, 851-857 (1996).
The paper contains a uniqueness theorem for the integral equation \[ \int^y_0 [u(x+h,\eta)+u(x-h,\eta)\frac{d\eta}{\sqrt{y-\eta}}+\int^y_0\int^{x+k}_{x-h} K(x,y,\xi,\eta)u(\xi,\eta)d\xi d\eta=f(x,y), \] where \(h=\sqrt{y-\eta}\) and \(K(x,y,\xi,\eta)=0\) for \(|\xi+x|\geq h\).

MSC:

53C65 Integral geometry
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References:

[1] K. Maurin, Methods of Hilbert Space [Russian translation], Mir, Moscow (1965).
[2] M. M. Lavrent’ev, ”On a certain class of integral geometry problems on the plane,” Sibirsk. Mat. Zh.,30, No. 4, 62–68 (1989).
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