# Atlantis Institut des Sciences Fictives

```000065248 001__ 65248
000065248 005__ 20190709135634.0
000065248 0247_ \$\$2doi\$\$a10.1093/imrn/rnw186
000065248 0248_ \$\$2sideral\$\$a104342
000065248 037__ \$\$aART-2017-104342
000065248 041__ \$\$aeng
000065248 100__ \$\$aGrünbaum, F.A.
000065248 245__ \$\$aThe CMV bispectral problem
000065248 260__ \$\$c2017
000065248 5060_ \$\$aAccess copy available to the general public\$\$fUnrestricted
000065248 5203_ \$\$aA classical result due to Bochner classifies the orthogonal polynomials on the real line which are common eigenfunctions of a second order linear differential operator. We settle a natural version of the Bochner problem on the unit circle which answers a similar question concerning orthogonal Laurent polynomials and can be formulated as a bispectral problem involving CMV matrices. We solve this CMV bispectral problem in great generality proving that, except the Lebesgue measure, no other one on the unit circle yields a sequence of orthogonal Laurent polynomials which are eigenfunctions of a linear differential operator of arbitrary order. Actually, we prove that this is the case even if such an eigenfunction condition is imposed up to finitely many orthogonal Laurent polynomials.
000065248 536__ \$\$9info:eu-repo/grantAgreement/ES/DGA/E64\$\$9info:eu-repo/grantAgreement/ES/MICINN/MTM2011-28952-C02-01\$\$9info:eu-repo/grantAgreement/ES/MINECO/MTM2014-53963-P