FUNCTIONS WHICH ARE ALMOST MULTIPLIERS OF HILBERT FUNCTION SPACES

JAMES AGLER NICHOLAS JOHN YOUNG

Abstract. We introduce a natural class of functions, the pseudomultipliers, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the 1-pseudomultipliers of Hilbert spaces of analytic functions under mild hypotheses.