Integrals and series of elementary functions
Integrals and series of elementary functions
Integrals and series of special functions
Integrals and series of special functions
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The k-dimensional totally geodesic Radon transform on the unit sphere S^n and the corresponding cosine transform can be regarded as members of the analytic family of intertwining fractional integrals R^@af(@x)=@c"n","k(@a)@!S^nf(x)sind(x,@x)^@a^+^k^-^ndx,d(x,@x) being the geodesic distance between x@?S^n and the k-geodesic @x. We develop a unified approach to the inversion of R^@af for all @a=0,1==2. The cases of smooth f and f@?L^p are considered. A series of new inversion formulas is obtained. The convolution-backprojection method is developed.