Advances in Theoretical and Mathematical Physics

Momentum transforms and Laplacians in fractional spaces

Gianluca Calcagni and Giuseppe Nardelli

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 20 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.atmp/1408559165

Mathematical Reviews number (MathSciNet)
MR3053972

Zentralblatt MATH identifier
1272.81080

Citation

Calcagni, Gianluca; Nardelli, Giuseppe. Momentum transforms and Laplacians in fractional spaces. Adv. Theor. Math. Phys. 16 (2012), no. 4, 1315--1348. https://projecteuclid.org/euclid.atmp/1408559165


Export citation