A Commutator Method for the Diagonalization of Hankel Operators

Dimitri R Yafaev (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

A method for the explicit diagonalization of some Hankel operators is presented. This method makes it possible to give new proofs of classical results on the diagonalization of Hankel operators with absolutely continuous spectrum and obtain new results. The approach relies on the commutation of a Hankel operator with a certain second-order differential operator.

Mots clés: Hankel operators; spectrum; eigenfunctions; explicit solutions; commutators

Domaines: Equations aux dérivées partielles [math.AP]

Dimitri R Yafaev. A Commutator Method for the Diagonalization of Hankel Operators. Functional Analysis and Its Applications, 2010, 44 (4), pp.295-306. ⟨10.1007/s10688-010-0040-z⟩. ⟨hal-00583008⟩