Accession Number:

ADA028157

Title:

The 'Fourier' Transform of a Resolution Space and a Theorem of Masani.

Descriptive Note:

Interim rept.,

Corporate Author:

TEXAS TECH UNIV LUBBOCK DEPT OF ELECTRICAL ENGINEERING

Personal Author(s):

Report Date:

1975-08-01

Pagination or Media Count:

7.0

Abstract:

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.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE