Implementations of Derivations on the Quantum Annulus
We construct compact parametrix implementations of covariant derivations on the quantum annulus.
math.OA↗
arXiv subjects
Kaoru Sakai
Publications and source records attributed to Kaoru Sakai.
Unbounded Derivations in Bunce-Deddens-Toeplitz Algebras
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 these derivations on associated GNS Hilbert spaces.
math.OA↗
A Value Region Problem for Continued Fractions and Discrete Dirac Equations
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 fractions with bounded ratio of consecutive elements, and show how those estimates control growth of solutions of a system of discrete Dirac equations.
math.NT↗
Derivations and Spectral Triples on Quantum Domains I: Quantum Disk
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 parametrices and thus can be used to define spectral triples.
math.OA↗
Spectral Triples for nonarchimedean local fields
Using associated trees, we construct a spectral triple for the C$^*$-algebra of continuous functions on the ring of integers $R$ of a nonarchimedean local field $F$ of characteristic zero, and investigate its properties. Remarkably, the spectrum of the spectral triple operator is closely related to the roots of a $q$-hypergeometric function. We also study a non compact version of this construction for the C$^*$-algebra of continuous functions on $F$, vanishing at infinity.
math.OA↗
A note on spectral properties of the $p$-adic tree
We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\mathbb Z_p$ via Michon's correspondence. We show that the spectrum is closely related to the roots of a certain $q-$hypergeometric function and discuss the analytic continuation of the zeta function associated with $D^*D$.
math.SP↗
The Quantum Pair of Pants
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 determine the structure of the $C^*$-algebra generated by that operator. The algebra can be considered as the quantum pair of pants.
math.OA↗