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


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.


Download Citation

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


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

zbMATH: 1272.81080
MathSciNet: MR3053972

Rights: Copyright © 2012 International Press of Boston

Vol.16 • No. 4 • August 2012
Back to Top