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dc.contributor.authorOngati, Naftali O.
dc.contributor.authorOleche, Paul O.
dc.contributor.authorAgure, John O.
dc.date.accessioned2016-06-16T08:21:56Z
dc.date.available2016-06-16T08:21:56Z
dc.date.issued2009
dc.identifier.citationVolume 52 No. 2en_US
dc.identifier.urihttp://ijpam.eu/contents/2009-52-2/2/2.pdf
dc.identifier.urihttp://62.24.102.115:8080/xmlui/handle/123456789/97
dc.description.abstractA bounded operator with the spectrum lying in a compact set V ⊂ R, has C∞(V ) functional calculus. On the other hand, an operator H acting on a Hilbert space H, admits a C(R) functional calculus if H is self-adjoint. So in a Banach space setting, we really desire a large enough intermediate topological algebra A, with C∞ 0 (R) ⊂ A ⊆ C(R) such that spectral operators or some sort of their restrictions, admit a A functional calculus. In this paper we construct such an algebra of smooth functions on R that decay like (√ 1 + x2) β as |x| → ∞, for some β < 0. Among other things, we prove that C∞ c (R) is dense in this algebra. We demonstrate that important functions like x 7→ e x are either in the algebra or can be extended to functions in the algebra. We characterize this algebra fully.en_US
dc.language.isoenen_US
dc.subjectBanach algebraen_US
dc.subjectsmooth functionen_US
dc.subjectextensionen_US
dc.titleThe algebra of smooth functions of rapid descenten_US
dc.typeArticleen_US


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