Absolute Continuity and the Uniqueness of the Constructive Functional Calculus
Douglas Bridges, Hajime Ishihara · Mathematical logic quarterly · 1994
Abstract The constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions. Mathematics Subject Classification: 03F60, 46S30, 47S30.