Dragilev’s theory of
regular bases in nuclear Fréchet spaces is applied to obtain necessary and
sufficient conditions in terms of the zeros for a linear Pincherle sequence to be a
basis for the space ℱR of functions analytic on the interior of the disk of
radius R ≦∞. It is shown that a linear Pincherle basis is always proper. All
possible phenomena for the basis radius of a linear Pincherle sequence are
exhibited. In this connection it is shown that for any finite R0> 0 there is a
sequence of analytic functions which is a basis for ℱR if and only if R ≦ R0 or
R = ∞.
