Momentum transforms and Laplacians in fractional spaces

Gianluca Calcagni; Giuseppe Nardelli

Momentum transforms and Laplacians in fractional spaces

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arxiv 1202.5383 v3 pith:MDXX6YDR submitted 2012-02-24 math-ph hep-thmath.MP

Gianluca Calcagni , Giuseppe Nardelli This is my paper

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We define an infinite class of unitary transformations between position 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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