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- W2593957634 abstract "Triangle partition maps form a family that includes many, if not most, well-known multidimensional continued fraction algorithms. This paper begins the exploration of the functional analysis behind the transfer operator of each of these maps. We show that triangle partition maps give rise to two classes of transfer operators and present theorems regarding the origin of these classes; we also present related theorems on the form of transfer operators arising from compositions of triangle partition maps. We then find eigenfunctions of eigenvalue 1 for transfer operators associated with select triangle partition maps on specified Banach spaces and show the existence of spectral gaps for select transfer operators. 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." @default.
- W2593957634 created "2017-03-16" @default.
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- W2593957634 date "2017-03-05" @default.
- W2593957634 modified "2023-09-27" @default.
- W2593957634 title "Functional Analysis behind a Family of Multidimensional Continued Fractions:: Triangle Partition Maps" @default.
- W2593957634 hasPublicationYear "2017" @default.
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