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

 

Hidden subspace algorithm in white noise analysis


Author: Jeremy J. Becnel
Journal: Trans. Amer. Math. Soc. 364 (2012), 5035-5055
MSC (2010): Primary 60H40; Secondary 81P68
Published electronically: April 30, 2012
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Abstract: In 2003, Professors Lomonaco and Kauffman developed an algorithm to find a hidden subspace of a functional. The algorithm was developed in the spirit of Feynman path integrals but lacked mathematical rigor. In this paper we make use of the framework of the White Noise Distribution Theory to supply the appropriate mathematical machinery to make the algorithm rigorous. In the process we construct a Gaussian measure for affine subspaces of a Hilbert space and develop a decomposition theorem for these measures.


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Additional Information

Jeremy J. Becnel
Affiliation: Department of Mathematics and Statistics, Stephen F. Austin State University, Nacogdoches, Texas 75962-3040
Email: becneljj@sfasu.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05661-3
PII: S 0002-9947(2012)05661-3
Keywords: White noise analysis, quantum computing, hidden subspace algorithm
Received by editor(s): July 21, 2010
Published electronically: April 30, 2012
Additional Notes: This research was supported by Stephen F. Austin Faculty Research Grant
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.