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An infinite-dimensional integral identity for the Segal-Bargmann transform

Author(s): Jeremy J. Becnel; Ambar N. Sengupta
Journal: Proc. Amer. Math. Soc. 135 (2007), 2995-3003.
MSC (2000): Primary 60H40; Secondary 46G12
Posted: May 9, 2007
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Abstract | References | Similar articles | Additional information

Abstract: We prove an infinite-dimensional integral identity equating the integral of a function on a subspace of a linear space to the integral of its Segal-Bargmann transform over the orthogonal complement.

References:

1.: Jeremy J. Becnel, Equivalence of topologies and Borel fields for countably-Hilbert spaces, Proceeding of the AMS 134 (2006), 581-590. MR 2176027 (2006j:57044)
2.: Lars Hörmander, The analysis of linear partial differential operators I, Grundlehren der mathematischen Wissenschaften, Springer-Verlag, Berlin, Heidelberg, 1983. MR 717035 (85g:35002a)
3.: Hui-Hsiung Kuo, White noise distribution theory, Probability and Stochastic Series, CRC Press, Inc., New York, New York, 1996. MR 1387829 (97m:60056)

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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

Ambar N. Sengupta
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803
Email: sengupta@math.lsu.edu

DOI: 10.1090/S0002-9939-07-08995-2
PII: S 0002-9939(07)08995-2
Received by editor(s): June 8, 2006
Posted: May 9, 2007
Additional Notes: Research supported by US NSF grant DMS-0201683 and DMS-0601141
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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