Questions tagged [gelfand-shilov-spaces]

The Gelfand Shilov Spaces are spaces of fundamental functions. Conditions are imposed on both the decrease of fundamental functions as well as the growth of their derivatives as $|x|\to \infty$.

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How to construct examples of functions in the Spaces of type $\mathcal{S}$

There are $3$ $\mathcal{S}$-type Spaces, namely $\mathcal{S}_\alpha\:,\: \mathcal{S}^\beta\:,\:\mathcal{S}_\alpha^\beta$. They are defined by: $\mathcal{S}_\alpha: |x^k\varphi^{(q)}(x)|\le C_qA^kk^{...