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

DOI

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

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - S.N.M. Ruijsenaars
PY  - 2005
DA  - 2005/12/01
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  - 10.2991/jnmp.2005.12.s2.19
ID  - Ruijsenaars2005
ER  -