6 citations · 15 across the 7 of their papers we have counts for
7 papers
Implementations of Derivations on the Quantum Annulus
Slawomir Klimek, Matt McBride, Kaoru Sakai
We construct compact parametrix implementations of covariant derivations on the quantum annulus.
Unbounded Derivations in Bunce-Deddens-Toeplitz Algebras
Slawomir Klimek, Matt McBride, Sumedha Rathnayake +2
In this paper we study decompositions and classification problems for unbounded derivations in Bunce-Deddens-Toeplitz and Bunce-Deddens algebras. We also look at implementations of…
Derivations and Spectral Triples on Quantum Domains I: Quantum Disk
Slawomir Klimek, Matt McBride, Sumedha Rathnayake +2
We study unbounded invariant and covariant derivations on the quantum disk. In particular we answer the question whether such derivations come from operators with compact parametri…
Spectral Triples for nonarchimedean local fields
Slawomir Klimek, Sumedha Rathnayake, Kaoru Sakai
Using associated trees, we construct a spectral triple for the C-algebra of continuous functions on the ring of integers of a nonarchimedean local field of characterist…
A note on spectral properties of the -adic tree
Slawomir Klimek, Sumedha Rathnayake, Kaoru Sakai
We study the spectrum of the operator , where the operator , introduced in \cite{KMR}, is a forward derivative on the -adic tree, a weighted rooted tree associated to $…
The Quantum Pair of Pants
Slawomir Klimek, Matt McBride, Sumedha Rathnayake +1
We compute the spectrum of the operator of multiplication by the complex coordinate in a Hilbert space of holomorphic functions on a disk with two circular holes. Additionally we d…
A Value Region Problem for Continued Fractions and Discrete Dirac Equations
Slawomir Klimek, Matt McBride, Sumedha Rathnayake +1
Motivated by applications in noncommutative geometry we prove several value range estimates for even convergents and tails, and odd reverse sequences of Stieltjes type continued fr…