Abstract
A theory of test function spaces is developed. These are generalizations of test function spaces of type Hμ. The elements of the dual spaces are called ultradistributions, It is shown that the Hankel transformation hμ for μ≧−1/2 is a continuous linear mapping from each of these spaces into certain spaces of the above type. The generalized Hankel transformation hμ′ is defined as a continuous linear mapping between the dual spaces. Hankel transformations of arbitrary order and also of arbitrary growth are studied. The theory thus developed is applied to prove a uniqueness theorem for the Cauchy problem for the operator Sμ.
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