Abstract
Let <TEX>$\mathcal{K}^{\prime}_M$</TEX> be the generalized tempered distributions of <TEX>$e^{M(t)}$</TEX>-growth, where the function M(t) grows faster than any linear functions as <TEX>${\mid}t{\mid}{\rightarrow}{\infty}$</TEX>, and let <TEX>$K^{\prime}_M$</TEX> be the Fourier transform spaces of <TEX>$\mathcal{K}^{\prime}_M$</TEX>. We obtain the relationship between certain classes of analytic functions in tubes, <TEX>$\mathcal{K}^{\prime}_M$</TEX> and <TEX>$K^{\prime}_M$</TEX>.
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