Monday, February 27, 2012

1202.5383 (Gianluca Calcagni et al.)

Momentum transforms and Laplacians in fractional spaces    [PDF]

Gianluca Calcagni, Giuseppe Nardelli
We define an infinite class of unitary transformations between configuration
and momentum fractional spaces, thus generalizing the Fourier transform to a
special class of fractal geometries. Each transform diagonalizes a unique
Laplacian operator. We also introduce a new version of fractional spaces, where
coordinates and momenta span the whole real line. In one topological dimension,
these results are extended to more general measures.
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