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.
|Number of pages||34|
|Journal||Advances in Theoretical and Mathematical Physics|
|Publication status||Published - 2012|
- Fractional field theory