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作者：BARCHIELLI, A; LUPIERI, G
作者单位：Istituto Nazionale di Fisica Nucleare (INFN)
摘要：In quantum mechanics certain operator-valued measures are introduced, called instruments, which are an analogue of the probability measures of classical probability theory. As in the classical case, it is interesting to study convolution semigroups of instruments on groups and the associated semigroups of probability operators. In this paper the case is considered of a finite-dimensional Hilbert space (n-level quantum system) and of instruments defined on a finite-dimensional Lie group. Then, ...
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作者：HALL, P; MARRON, JS
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：This paper establishes asymptotic lower bounds which specify, in a variety of contexts, how well (in terms of relative rate of convergence) one may select the bandwidth of a kernel density estimator. These results provide important new insights concerning how the bandwidth selection problem should be considered. In particular it is shown that if the error criterion is Integrated Squared Error (ISE) then, even under very strong assumptions on the underlying density, relative error of the select...
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作者：JORGENSEN, PET; POWERS, RT
作者单位：University of Pennsylvania
摘要：Let U denote the extended Weyl algebra, U0 subset-of U, the Weyl algebra. It is well known that every element of U of the form A = SIGMA-B(k)* B(k) is positive. We prove that the converse implication also holds: Every positive element A in U has a quadratic sum factorization for some finite set of elements (B(k)) in U. The corresponding result is not true for the subalgebra U0. We identify states on U0 which do not extend to states on U. It follows from a result of Powers (and Arveson) that su...
