Functional analysis behind a Family of Multidimensional Continued Fractions: Part II
Abstract
This paper is a direct continuation of "Functional analysis behind a Family of Multidimensional Continued Fractions: Part I," in which we started the exploration of the functional analysis behind the transfer operators for triangle partition maps, a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This allows us now to find eigenfunctions of eigenvalue 1 for transfer operators associated with select triangle partition maps on specified Banach spaces. We proceed to prove that the transfer operators, viewed as acting on one-dimensional families of Hilbert spaces, associated with select triangle partition maps are nuclear of trace class zero. We finish by deriving Gauss-Kuzmin distributions associated with select triangle partition maps.
Keywords
Cite
@article{arxiv.2008.07938,
title = {Functional analysis behind a Family of Multidimensional Continued Fractions: Part II},
author = {Ilya Amburg and Thomas Garrity},
journal= {arXiv preprint arXiv:2008.07938},
year = {2020}
}
Comments
To appear in Publicationes Mathematicae Debrecen. This is the second half of the earlier arXiv:1703.01589, which has been split into two under the recommendation of the journal. This also includes eleven pages of tables of formulas that will not be in the published version