Journal of Nonlinear Mathematical Physics

Volume 12, Issue Supplement 2, December 2005, Pages 253 - 294

A unitary joint eigenfunction transform for the AOs exp(ia±d/dz) + exp(2z/a)

Authors
S N M RUIJSENAARS
Corresponding Author
S N M RUIJSENAARS
Available Online 1 December 2005.
DOI
https://doi.org/10.2991/jnmp.2005.12.s2.19How to use a DOI?
Abstract
For positive parameters a+ and a- the commuting difference operators exp(ia±d/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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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
12 - 100
Pages
253 - 294
Publication Date
2005/12
ISBN
91-974824-5-5
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2005.12.s2.19How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - S N M RUIJSENAARS
PY  - 2005
DA  - 2005/12
TI  - A unitary joint eigenfunction transform for the AOs exp(ia±d/dz) + exp(2z/a)
JO  - Journal of Nonlinear Mathematical Physics
SP  - 253
EP  - 294
VL  - 12
IS  - Supplement 2
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.s2.19
DO  - https://doi.org/10.2991/jnmp.2005.12.s2.19
ID  - RUIJSENAARS2005
ER  -