The 'Fourier' Transform of a Resolution Space and a Theorem of Masani.
TEXAS TECH UNIV LUBBOCK DEPT OF ELECTRICAL ENGINEERING
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Using two classic theorems one of Mackey and another of Stone and a recent result of Masani and Rosenberg, this paper pieces together a generalized frequency response theory for an abstract Uniform Resolution Space. The present theory assimilates past work as done by Falb, Freedman, Anton, Masani and Rosenberg, and one of the authors. The results of this paper are not new, but are merely a rearrangement of subtleties uncovered by the aforementioned authors. An interesting consequence of this work was that an abstract Uniform Resolution Space has both a time transform and a frequency transform. Such a duality is not readily identifiable in an L sub 2 function space since the time transform, there, is the identity.
- Numerical Mathematics