RT Journal Article
T1 An extension of Bochner's problem: exceptional invariant subspaces
A1 Gómez-Ullate Otaiza, David
A1 Kamran, Niky
A1 Milson, Robert
AB We prove an extension of Bochner's classical result that characterizes the classical polynomial families as eigenfunctions of a second-order differential operator with polynomial coefficients. The extended result involves considering differential operators with rational coefficients and the requirement is that they have a numerable sequence of polynomial eigenfunctions p(1), p(2),.. of all degrees except for degree zero. The main theorem of the paper provides a characterization of all such differential operators. The existence of such differential operators and polynomial sequences is based on the concept of exceptional polynomial subspaces, and the converse part of the main theorem rests on the classification of codimension one exceptional subspaces under projective transformations, which is performed in this paper.
PB Academic Press-Elsevier Science
SN 0021-9045
YR 2010
FD 2010-05
LK https://hdl.handle.net/20.500.14352/44631
UL https://hdl.handle.net/20.500.14352/44631
LA eng
NO © 2009 Elsevier Inc.We thank Peter Crooks for reviewing the manuscript and providing many useful remarks. We are also grateful to Jorge Arvesú, Norrie Everitt, Mourad Ismail, Francisco Marcellán, Lance Littlejohn and André Ronveaux for their helpful comments on the manuscript. This work was supported in part by the Ramón y Cajal program of the Spanish Ministry of Science and Technology; the Dirección General de Investigación [grants MTM2006-00478 and MTM2006- 14603 to D.G.U.] and the National Science and Engineering Reserach Council of Canada [grants RGPIN 105490- 2004 to N.K. and RGPIN-228057-2004 to R.M.]
NO Spanish Ministry of Science and Technology; Direccion General de Investigacion
NO National Science and Engineering Research Council of Canada
DS Docta Complutense
RD 8 abr 2025