Sufficient conditions for the absence of absolutely continuous spectrum for unbounded Jacobi operators are given. A class of unbounded Jacobi operators with purely singular continuous spectrum is constructed as well.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-5, author = {Petru Cojuhari and Jan Janas}, title = {Unbounded Jacobi Matrices with Empty Absolutely Continuous Spectrum}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, volume = {56}, year = {2008}, pages = {39-51}, zbl = {1156.47033}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-5} }
Petru Cojuhari; Jan Janas. Unbounded Jacobi Matrices with Empty Absolutely Continuous Spectrum. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 39-51. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-5/