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Absolute Continuity and the Uniqueness of the Constructive Functional Calculus
Author(s) -
Bridges Douglas,
Ishihara Hajime
Publication year - 1994
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19940400408
Subject(s) - mathematics , constructive , orthonormal basis , constructive proof , uniqueness , absolute continuity , hilbert space , calculus (dental) , pure mathematics , separable space , algebra over a field , discrete mathematics , mathematical analysis , computer science , medicine , physics , dentistry , process (computing) , quantum mechanics , operating system
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.