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arXiv · 1206.6553

Equality of uniform and Carleman spectra for bounded measurable functions

Bolis Basit·Alan J. Pryde
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Abstract

In this paper we study various types of spectra of functions $ϕ:\jj\to X$, where $\jj\in\{\r_+,\r\}$ and $X$ is a complex Banach space. We show that uniform spectrum defined in [15] coincides with Carleman spectrum for $ϕ\in L^{\infty}(\r,X)$. This result holds true also for Laplace (half-line) spectrum for $ϕ\in L^{\infty}(\r_+,X)$. We also indicate a class of bounded measurable functions for which Laplace spectrum and Carleman spectrum are equal

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Bolis Basit, Alan J. Pryde. 2012-06-28. Equality of uniform and Carleman spectra for bounded measurable functions. https://arxiv.org/abs/1206.6553

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