  We consider frames F in a given Hilbert space, and we show that every F may
be obtained in a constructive way from a reproducing kernel and an orthonormal
basis in an ambient Hilbert space. The construction is operator-theoretic,
building on a geometric formula for the analysis operator defined from F. Our
focus is on the infinite-dimensional case where a priori estimates play a
central role, and we extend a number of results which are known so far only in
finite dimensions. We further show how this approach may be used both in
constructing useful frames in analysis and in applications, and in
understanding their geometry and their symmetries.
