A characterization of the spaces $S%5E{k/k+1}_{1/k+1}$ by means of holomorphic semigroups
S.J.L. van Eijndhoven, J. de Graaf, R. S. Pathak · Eindhoven University of Technology : Dept of Mathematics : memorandum · 1982
The Gel’fand–Shilov spaces $\mathfrak{S}_\alpha ^\beta ,{\alpha = 1}/ {(k + 1)},{\beta = k} /{(k + 1)}$, are special cases of a general type of test function spaces introduced by de Graaf. We give a self-adjoins operator so that the test functions in those $\mathfrak{S}_\alpha ^\beta $ spaces can be expanded in terms of the eigenfunctions of that self-adjoins operator.