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In addition, we define a set of fine grid basis functions with twice the cutoff frequency as the :

(53) 
that correspond to a planewave representation that has twice the wavevector cutoff of the standard basis functions.
are the points of the fine grid. This basis is localised on the grid points of the fine grid and is also orthogonal:
and satisfies a property analogous to equation (52):
where
is a version of the function that is bandwidth limited to the same frequencies as the basis functions .
Next: Bibliography
Up: Basis Set
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Peter D. Haynes
20021029