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Superfunctions and the Algebra of Subspace Collections and Their Association with Rational Functions of Several Complex Variables by Milton, Graeme W. is a scholarly article available to read on EtoBox.

What is Superfunctions and the Algebra of Subspace Collections and Their Association with Rational Functions of Several Complex Variables about?

A natural connection between rational functions of several real or complex variables, and subspace collections is explored. A new class of function, superfunctions, are introduced which are the counterpart to functions at the level of subspace collections. Operations on subspace collections are found to correspond to various operations on rational functions, such as addition, multiplication and substitution. It is established that every rational matrix valued function which is homogeneous of degree 1 can be generated from an appropriate, but not necessarily unique, subspace collection: the mapping from subspace collections to rational functions is onto, but not one to one. For some applications superfunctions may be more important than functions, as they incorporate more information about the physical problem, yet can be manipulated in much the same way as functions. Previously subspace collections had been introduced when there was an inner product on the vector (or Hilbert) space, and appropriate subspaces were mutually orthogonal. In that setting certain normalization and reduction operations on subspace collections led to a continued fraction expansion of the associated functio

Author

Milton, Graeme W.

Published

2015

Language

EN