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# Closed and Exact Functions in the Context of Ginzburg--Landau Models

Published:2008-06-01
Printed: Jun 2008
• Anamaria Savu
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## 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}

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