Arising of Bergman reproducing kernel in Bose-Fock space
DOI:
https://doi.org/10.22199/S07160917.1998.0002.00006Abstract
We introduce a Bose-Fock space A (Dd) of anti-holomorphic complex-valued functions on the unit polydisc Dd in Cd, with d ? NU {?}.
A unitary isomorphism U from the abstract Bose-Fock space ?H to A ( Dd) is produced, and it is shown that U transforms twisted coherent vectors into Bergman kernels in Dd.
References
[1] B.C. Hall, The Segal-Bargmann "Coherent State" Transform for Compact Lie Groups, J. Funct. Anal. 122 (1994) 103-151.
[2] E. Nelson, Probability theory and euclidean field theory, Lecture Notes in Phys. 25 (1973), 94-124, Springer-Verlag.
[3] T.T. Nielsen, Base Algebras: The Complex and Real Wave Representations, Lecture Notes in Math. 1472 (1991), Springer-Verlag.
[4] K. Seip, Reproducing formulas and double orthogonality in Bargmann and Bergman spaces, Siam J. Math. Anal., Vol. 22, No. 3, (1991) 856-876.
[5] W. Slowikowski, Infinite dimensional Lie algebras and Lie groups of operators for paired quantum particles, to appear. slowi@mi.aau.dk.
[2] E. Nelson, Probability theory and euclidean field theory, Lecture Notes in Phys. 25 (1973), 94-124, Springer-Verlag.
[3] T.T. Nielsen, Base Algebras: The Complex and Real Wave Representations, Lecture Notes in Math. 1472 (1991), Springer-Verlag.
[4] K. Seip, Reproducing formulas and double orthogonality in Bargmann and Bergman spaces, Siam J. Math. Anal., Vol. 22, No. 3, (1991) 856-876.
[5] W. Slowikowski, Infinite dimensional Lie algebras and Lie groups of operators for paired quantum particles, to appear. slowi@mi.aau.dk.
Published
2018-04-04
How to Cite
[1]
O. Rask, “Arising of Bergman reproducing kernel in Bose-Fock space”, Proyecciones (Antofagasta, On line), vol. 17, no. 2, pp. 215-226, Apr. 2018.
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