Arising of Bergman reproducing kernel in Bose-Fock space

Authors

  • Olé Rask Universidad Austral de Chile.

DOI:

https://doi.org/10.22199/S07160917.1998.0002.00006

Abstract

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.

Author Biography

Olé Rask, Universidad Austral de Chile.

Instituto de Matemáticas.

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.

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.

Issue

Section

Artículos