S.J.L. van Eijndhoven

Some results on Hankel invariant distribution spaces

Abstract Three Hankel invariant test function spaces and the associated generalized function spaces are introduced. The elements of the respective test function spaces are described both in functional analytic and in classical analytic terms. It is shown that one of the test function spaces equals the space Hμ of Zemanian.

Trajectory spaces, generalized functions and unbounded operators

Prologue.- Analyticity spaces, trajectory spaces and linear mappings between them.- Illustrative examples of analyticity spaces.- Compound spaces, tensor products and kernel theorems.- Algebras of continuous linear mappings on analyticity spaces and trajectory spaces.- A mathematical interpretation of Diracs formalism for quantum mechanics.