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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Positive forms and dilations


Author: Wacław Szymański
Journal: Trans. Amer. Math. Soc. 301 (1987), 761-780
MSC: Primary 47A20; Secondary 42A70, 43A35, 47D05
MathSciNet review: 882714
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Abstract: By using the quadratic form and unbounded operator theory a new approach to the general dilation theory is presented. The boundedness condition is explained in terms of the Friedrichs extension of symmetric operators. Unbounded dilations are introduced and discussed. Applications are given to various problems involving positive definite functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0882714-0
PII: S 0002-9947(1987)0882714-0
Keywords: Positive quadratic forms, the Friedrichs extension of a positive operator, positive definite function, dilation, $ \ast$-dilation, moment problem, reconstruction of quantum mechanics
Article copyright: © Copyright 1987 American Mathematical Society