Üç boyutlu uzayda Volterra tipindeki, zayıf nokorrekt integral geometri problemi

Abstract

Bu makalede küre ailesinden uzaydaki bır fonksiyonnu kurtarılma problemi ele alınmaktadır. Volterranin önce birinci sonra ikinci tür integral denklemine getırmek yoluyla kanıtlanır. Furier değiştirme yöntemleri de kullanılmaktadır. Üç boyutlu uzayda Volterra tipindeki operatör denklemlerinin bazı yeni sınıfları için teklik teoremleri kanıtlanmıştır.

Keywords

• İntegral geometri problemi
• Fourier değiştirilmesi
• teklik teoremi
• Volterra integral denklemi

Weekly Ill-posed integral geometry problems of Volterra type in three-dimensional space

Abstract

In this paper considers the problem of recovering a function from families of spheres in space. The uniqueness of the solution of the problem is proved by reducing it to the Volterra integral equation of the first and then the second kind. Fourier transform methods are also used. Uniqueness theorems are proved for some new classes of operator equations of Volterra type in three-dimensional space.

Keywords

• Integral geometry problem
• Fourier transform
• uniqueness theorem
• Volterra integral equation.

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