PROPERTIES OF MULTIPLIERS ON SPECIAL ALGEBRAS WITH APPLICATION TO SIGNAL PROCESSING

Lucian Flavius PATER

Abstract


In many cases, signal processing methods cannot be circumscribed to existing models but require some extensions of mathematical theories (operator theory, functional analysis) to enable the widening of more general spaces or the modeling using more general functions but with fewer properties satisfying theorems used in similar models. In this context, one can expand the Hilbert space L2 to a locally convex space, sequentially complete, extension required in terms of types of data that must be processed. Hence, there is a need to obtain some medium ergodic theorems which can characterize operators endowed with a certain type of limitation. In 1943, Dunford obtained ergodic theorems using analytical calculation of the operational functions of a complex Banach space operator. In 1974, M. Lin added an equivalent condition to the uniform ergodic theorem .In this paper, a study on some equivalent conditions for T (where T is a multiplier on a locally convex algebra A which has a closed range) is performed.

 Key words: multipliers, locally convex algebra, relatively regular operator, barreled space

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References


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