Advances in Theoretical and Mathematical Physics

Momentum transforms and Laplacians in fractional spaces

Gianluca Calcagni and Giuseppe Nardelli

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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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Adv. Theor. Math. Phys., Volume 16, Number 4 (2012), 1315-1348.

First available in Project Euclid: 20 August 2014

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Calcagni, Gianluca; Nardelli, Giuseppe. Momentum transforms and Laplacians in fractional spaces. Adv. Theor. Math. Phys. 16 (2012), no. 4, 1315--1348.

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