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Closed and Exact Functions in the Context of Ginzburg--Landau Models |
Canad. J. Math. 60(2008), 685-702
Published:2008-06-01
Printed: Jun 2008
Printed: Jun 2008
- Anamaria Savu
Abstract
For a general vector field we exhibit two Hilbert spaces, namely
the space of so called \emph{closed functions} and the space of \emph{exact functions}
and we calculate the codimension of the space of exact functions
inside the larger space of closed functions.
In particular we provide a new approach for the known cases:
the Glauber field and the second-order Ginzburg--Landau field
and for the case of the fourth-order Ginzburg--Landau field.
| Keywords: | Hermite polynomials, Fock space, Fourier coefficients, Fourier transform, group of symmetries |
| MSC Classifications: |
42B05 - Fourier series and coefficients 81Q50 - Quantum chaos [See also 37Dxx] 42A16 - Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30} |