title: |
A unitary joint eigenfunction transform for the AOs exp(iaħd/dz) + exp(2z/a) |
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publication: |
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| volume-issue: | 12 - Supplement 2 | |
| pages: | 253 - 294 | |
ISSN: |
1402-9251 | |
DOI: |
doi:10.2991/jnmp.2005.12.s2.19 (how to use a DOI) | |
author(s): |
S N M RUIJSENAARS |
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publication date: |
December 2005 |
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abstract: |
For positive parameters a+ and a- the commuting difference operators exp(iaħd/dz)
+ exp(2z/a), acting on meromorphic functions f(z), z = x + iy, are formally
self-adjoint on the Hilbert space H = L2
(R, dx). Volkov showed that they admit
joint eigenfunctions. We prove that the joint eigenfunctions for positive eigenvalues
exp(2p/a), p R, give rise to a unitary transform, thus associating commuting
self-adjoint operators on H to the analytic difference operators.
Contents |
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copyright: |
İ
Atlantis Press. This is an open-access article distributed under the
terms of the Creative Commons Attribution License, which permits
non-commercial use, distribution and reproduction in any medium,
provided the original work is properly cited. |
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full text: |