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Acta Mathematica Vietnamica

SPECTRAL CRITERIA OF ABSTRACT FUNCTIONS; INTEGRAL AND DIFFERENCE PROBLEMS

ALAA E. HAMZA, GILBERT L. MURAZ

Abstract

Let X be a complex Banach space and let M be a closed subspace of L(J,X), where J{R,R+}. We answer the following question: Under what conditions ϕsϕM sJ implies that ϕM. Some conditions will be imposed on M to obtain the main result concerning the indefinite integral. These conditions guarantee the following implication: FE(J,X)FM, where F is the integral 0tf(s)ds of fMCub(J,X). Also, we generalize Loomis' Theorem for almost periodic functions [19, Theorem 5], to a more general class of functions ML(R,X) containing AP(R,X). The main result of Part IV is: If ϕ is uniformly continuous, bounded, such that the M-spectrum σM(ϕ) of ϕ is at most countable and, for every λσM(ϕ), the function eiλtϕ(t) is ergodic, then ϕM.

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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
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      Metadata
      Backtrace
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      Metadata
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