Generalized Fock spaces, interpolation, multipliers, circle geometry.
By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane C which are square integrable with respect to a weight of the type e, where Q(z) is a quadratic form such that tr Q > 0. Each such space is in a natural way associated with an (oriented) circle in C. We consider the problem of interpolation between two Fock spaces. If and are the corresponding circles, one is led to consider the pencil of circles generated by and . If H is the...