Generalizations of the Watson transforms Public Deposited

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  • The generalized Hankel transforms are studied in the first part of this thesis; these include the Watson transforms as a special case. For the validity of the reciprocal relations, a necessary and sufficient condition on the kernel is proved. The proof involves first changing the variables so that all the relations can be written in the form of convolutions, and then applying the Fourier- Plancherel transforms to reduce the transcendental equations to simple algebraic equations. In the second part of the thesis, unitary mappings on the Hilbert space of square-integrable functions are characterized "analytically". A specialization of the kernels appearing in these analytic formulas yields the Watson transforms. A theorem on obtaining new pairs of kernels from two pairs of known ones is proved.
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