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Abstract
The convolution type summability reconstruction method via Radon transform data was introduced in (11) and extended in (12, 13, 16). This method totally depends upon the selection of radial polynomial convolution kernel K and the construction of the corresponding modified kernels $h\sb{i}$'s.
In this thesis, we introduce two families of positive radial polynomial kernels which are expressed in terms of the classical Jacoby polynomials. We show that the new positive radial polynomial kernels satisfy certain moment conditions and construct several types of the corresponding modified kernels which are conveniently written in terms of the Chebychev polynomials of the second kind. The resulting approximate reconstruction is asymptotically optimal.
