The classical theory of Toeplitz operators in spaces of analytic functions
deals usually with symbols that are bounded measurable functions on the domain
in question. A further extension of the theory was made for symbols being
unbounded functions, measures, and compactly supported distributions, all of
them subject to some restrictions.
In the context of a reproducing kernel Hilbert space we propose a certain
framework for a `maximally possible' extension of the notion of Toeplitz
operators for a `maximally wide' class of `highly singular' symbols. Using the
language of sesquilinear forms we describe a certain common pattern for a
variety of analytically defined forms which, besides covering all previously
considered cases, permits us to introduce a further substantial extension of a
class of admissible symbols that generate bounded Toeplitz operators.
Although our approach is unified for all reproducing kernel Hilbert spaces,
for concrete operator consideration in this paper we restrict ourselves to
Toeplitz operators acting on the standard Fock (or Segal-Bargmann) space