Search: MSC category 42A16
( Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30} )
1. CJM 2011 (vol 63 pp. 689)
 Olphert, Sean; Power, Stephen C.

Higher Rank Wavelets
A theory of higher rank multiresolution analysis is given in the
setting of abelian multiscalings. This theory enables the
construction, from a higher rank MRA, of finite wavelet sets
whose multidilations have translates forming an orthonormal basis
in $L^2(\mathbb R^d)$. While tensor products of uniscaled MRAs provide
simple examples we construct many nonseparable higher rank
wavelets. In particular we construct \emph{Latin square
wavelets} as rank~$2$ variants of Haar wavelets. Also we construct
nonseparable scaling functions for rank $2$ variants of Meyer
wavelet scaling functions, and we construct the associated
nonseparable wavelets with compactly supported Fourier transforms.
On the other hand we show that compactly supported scaling
functions for biscaled MRAs are necessarily separable.
Keywords: wavelet, multiscaling, higher rank, multiresolution, Latin squares Categories:42C40, 42A65, 42A16, 43A65 

2. CJM 2008 (vol 60 pp. 685)
 Savu, Anamaria

Closed and Exact Functions in the Context of GinzburgLandau Models
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 secondorder GinzburgLandau field
and for the case of the fourthorder GinzburgLandau field.
Keywords:Hermite polynomials, Fock space, Fourier coefficients, Fourier transform, group of symmetries Categories:42B05, 81Q50, 42A16 

3. CJM 2003 (vol 55 pp. 1019)
 Handelman, David

More Eventual Positivity for Analytic Functions
Eventual positivity problems for real convergent Maclaurin series lead
to density questions for sets of harmonic functions. These are solved
for large classes of series, and in so doing, asymptotic estimates are
obtained for the values of the series near the radius of convergence
and for the coefficients of convolution powers.
Categories:30B10, 30D15, 30C50, 13A99, 41A58, 42A16 
