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arXiv · 2008.07938

Functional analysis behind a Family of Multidimensional Continued Fractions: Part II

Ilya Amburg·Thomas Garrity
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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.

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Ilya Amburg, Thomas Garrity. 2020-08-18. Functional analysis behind a Family of Multidimensional Continued Fractions: Part II. https://arxiv.org/abs/2008.07938

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