Approximate Complexity and Functional Representation.
Technical summary rept.,
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Results are obtained dealing with the exact and the approximate representation of a function F as a superposition, in designated formats, of functions of fewer variables. Two main cases are considered. In the classical nomographic case one seeks criteria for deciding if a function can be expressed in the form fphix psiy, or as a uniform limit of such functions. The second case is also related to the solution of Hilberts 13th problem, and deals with the format Fx fphix where x lies in an n-cell I and phi is a real valued continuous function on I, and f is a function on R taking values in a chosen normed space epsilon. The use of these criteria is illustrated with several specific functions.
- Theoretical Mathematics