Banach-Space Valued Distributional Signals and Pseudo Signals

Abstract

This paper studies Banach-space valued distributional signals. The product of distributional signals is defined. The pseudo signal Pf ((x^−r₊). δ(^r-1) (x)} is obtained by the method of extracting finite part from divergent integral. A theorem for the stability of a linear continuous time invariant casual system is proved in Banach space valued tempered sense.

Indexing terms:

• Signals
• Pseudo signals
• System
• Banach space
• Impulse function