A generalization of the Müntz–Szász theorem to floating exponents with applications to Gauss- and Slater-type functions

The Müntz–Szász condition for completeness of the monomials xλn in L2 is extended to floating functions, where the exponents λn may depend on the number of basis functions used in an approximation. The generalized condition is rewritten for Gauss- and Slater-type functions and then discussed, especially with respect to even-tempered functions.