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A Dilation Theory Approach to Cubature Formulas. II
Author(s) -
Putinar Mihai
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200003)211:1<159::aid-mana159>3.0.co;2-r
Subject(s) - mathematics , hilbert space , dilation (metric space) , parametrization (atmospheric modeling) , computation , tuple , multivariate statistics , pure mathematics , commutative property , interpretation (philosophy) , algebra over a field , discrete mathematics , combinatorics , statistics , algorithm , physics , quantum mechanics , computer science , programming language , radiative transfer
An interpretation of multivariate cubature formulas for positive measures in terms of Hilbert space operators leads to a parametrization of all finite‐rank, cyclic and commutative dilations of a given cyclic tuple of self‐adjoint operators. Explicit matricial formulas for these dilations are presented; the abstract dilation problem suggested by the concrete computations is stated at the end of the note.