  Methods are described for the solution of linear inference problems subject
to deterministic constraints. The theory is motivated by, and illustrated with,
the estimation of a finite number of a function's spherical harmonic
coefficients from a finite set of its point values. Emphasis is placed on the
formulation and practical solution of problems within an infinite-dimensional
setting, and the role played by the model space topology. The application of
probabilistic constraints will be described in the sequel.
