Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8256003 | Journal of Geometry and Physics | 2016 | 15 Pages |
Abstract
A set of reproducing kernel Hilbert spaces are obtained on Hilbert spaces over quaternion slices with the aid of coherent states. It is proved that the so obtained set forms a measurable field of Hilbert spaces and their direct integral appears again as a reproducing kernel Hilbert space for a bigger Hilbert space over the whole quaternions. Hilbert spaces over quaternion slices are identified as representation spaces for a set of irreducible unitary group representations and their direct integral is shown to be a reducible representation for the Hilbert space over the whole quaternion field.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
B. Muraleetharan, K. Thirulogasanthar,