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Bargmann-Fock space

(Definition)

The Bargmann-Fock space (or simply Fock space) is the Hilbert space of entire functions, $\mathcal{F}^2(\mathbb{C})$ s.t.

$\displaystyle \int_\mathbb{C}\vert F(z)\vert^2 e^{- \pi \vert z\vert^2}dx dy<\infty$

with associated inner product

$\displaystyle \int_\mathbb{C}F(z)\overline{G(z)}e^{- \pi \vert z\vert^2}dx dy$

where

Bibliography

1: V. Bargmann, ``Remarks on a Hilbert Space of Analytic Function'' Proceedings of the National Academy of Sciences of the United States of America 48 (1962): 199 - 204
2: V. Bargmann & I. T. Todorov, ``Spaces of analytic functions on a complex cone as carriers for the symmetric tensor representations of SO(n)'' Journal of Mathematical Physics 18 6 (1977): 1141 - 1148

"Bargmann-Fock space" is owned by ErlendA.

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Other names:

Fock space

Also defines:

Fock space

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Cross-references: inner product, entire functions, Hilbert space
There are 3 references to this entry.

This is version 11 of Bargmann-Fock space, born on 2007-02-19, modified 2007-02-21.
Object id is 8928, canonical name is BargmannFockSpace.
Accessed 1856 times total.

Classification:

43A15 (Abstract harmonic analysis :: $L^p$-spaces and other function spaces on groups, semigroups, etc.)

Pending Errata and Addenda

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