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

Equality of uniform and Carleman spectra for bounded measurable functions