Problem Of Integral Geometry Research Articles

The problem of integral geometry on the group Pn(k) and its application to the theory of representations

The problem of integral geometry on the group Pn(k) and its application to the theory of representations

An inverse problem for a parabolic equation and a problem of integral geometry

An inverse problem for a parabolic equation and a problem of integral geometry

A problem of integral geometry and the inverse problem for a parabolic equation

A problem of integral geometry and the inverse problem for a parabolic equation

Some integral-geometry problems

Some integral-geometry problems

On some classes of uniqueness for the solution of integral geometry problems

We consider the problem of determining a function from a knowledge of integrals of the function along families of curves with a known weight function. For sufficiently general assumptions on the family of curves and on the weight function the problem is reduced to the solution of an integrodifferential equation. We establish the uniqueness of the solution of this equation in certain classes of functions.

On some problems of integral geometry

On some problems of integral geometry

A problem of integral geometry and a linearized inverse problem for a hyperbolic equation

A problem of integral geometry and a linearized inverse problem for a hyperbolic equation

Unitary representations of groups of automorphisms of riemann symmetric spaces of null curvature

Kalgebra ~ , and G is the corresponding compact form. We shall not discuss this here. In the present article we shall study unitary representations of the group ~ : we shall calculate their character (section 3 below), the Plancherel measure on the group (section 4) and on a symmetric space (section 5), we shall study zonal harmonics for r epresentations of class 1 (section 6), and we shall consider a problem of integral geometry in Euclidean space which arises from representations of the group ~ (section 7). The formulas for the representations of the groups 5 , G, G K have much in common. The questions listed above for the groups G K are studied in the classical works of G. Weyl; for the groups G many of them have not yet been completely answered(Planche rel's formula integral geometry on symmetric spaces of negative curvature).