Titlebook: Integral Geometry and Convolution Equations; V. V. Volchkov Book 2003 Springer Science+Business Media Dordrecht 2003 Fourier transform.con

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Some Classes of FunctionsLet . be a non-empty set and let . be a sigma algebra of subsets in .. Let . be a measure on .. Assume that . is a non-empty .-measurable subset in .. For . ∈ [1, +∞) we denote by ..(.) the collection of all .-measurable functions .: . → ? such that

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Some Special FunctionsWe give here some properties of gamma function which will be used later.

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Some Results Related to Spherical HarmonicsLet ., . ? 2 denotes the set of all homogeneous harmonic polynomials on ?. of degree .. A spherical harmonic of degree . is the restriction to . of an element of .. The collection of all spherical harmonics of degree . will be denoted by .. We note that . and . are a complex vector spaces. In addition, these spaces are invariant under rotations.

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Functions with Zero Integrals Over Spherical CapsThe necessary information which will be needed for proofs of theorems on spherical means on the sphere . are given in this chapter.

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