ORTHOGONALLY SCATTERED MEASURES.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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The report gives a coherent account of countably additive orthogonally scattered measures with values in a Hilbert space, and of the integration of complex-valued functions with respect to such measures. Some lacunae in the theory are cleared up. It is shown how the use of the concept of a basic orthogonally scattered measure in problems amenable to Hilbert space methods yields a unified treatment of the continuous and discrete aspects of such problems. The Fourier-Plancherel transformation over locally compact abelian groups is treated from this standpoint, and its bearing on the continuous eigenfunction expansions encountered in scattering theory is indicated. Author
- Statistics and Probability