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Journal Article

Momentum transforms and Laplacians in fractional spaces

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons4348

Calcagni,  G.
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1202.5383v2.pdf
(Preprint), 311KB

1408559165.pdf
(Any fulltext), 242KB

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Citation

Calcagni, G., & Nardelli, G. (2012). Momentum transforms and Laplacians in fractional spaces. Advances in Theoretical and Mathematical Physics, 16(4), 1315-1348.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-3B79-1
Abstract
We define an infinite class of unitary transformations between configuration 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.