Abstract
A fundamental problem is to determine the invariant subspaces of any given transformation and to write the transformation as an integral in terms of invariant subspaces. The aim of the paper is to add an example to the list of transformations with known invariant subspaces. The determination of invariant subspaces is a difficult problem which cannot be solved unless the transformation has special properties which aid the computation. Such transformations are found in connection with the theory of the hypergeometric function. The transformations which we study are unbounded and partially defined. Before we can think of solving the structure problem for such a transformation, we have to clarify the meaning of “invariant subspace”. We do this using the theory of Hilbert spaces whose elements are entire functions and which have these properties:
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