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August 2012 Momentum transforms and Laplacians in fractional spaces
Gianluca Calcagni, Giuseppe Nardelli
Adv. Theor. Math. Phys. 16(4): 1315-1348 (August 2012).

Abstract

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.

Citation

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Gianluca Calcagni. Giuseppe Nardelli. "Momentum transforms and Laplacians in fractional spaces." Adv. Theor. Math. Phys. 16 (4) 1315 - 1348, August 2012.

Information

Published: August 2012
First available in Project Euclid: 20 August 2014

zbMATH: 1272.81080
MathSciNet: MR3053972

Rights: Copyright © 2012 International Press of Boston

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Vol.16 • No. 4 • August 2012
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