Browsing by Author "Rathnayake, Sumedha"

Now showing 1 - 3 of 3
  • Thumbnail Image
    Item
    Derivations and Spectral Triples on Quantum Domains I: Quantum Disk
    (2017) Klimek, Slawomir; McBride, Matt; Rathnayake, Sumedha; Sakai, Kaoru; Wang, Honglin; Mathematical Sciences, School of Science
    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.
  • Thumbnail Image
    Item
    A note on spectral properties of the p-adic tree
    (AIP, 2016) Klimek, Slawomir; Rathnayake, Sumedha; Sakai, Kaoru; Department of Mathematical Sciences, School of Science
    We study the spectrum of the operator D∗D, where the operator D, introduced in Klimek et al. [e-print arXiv:1403.7263v2], is a forward derivative on the p-adic tree, a weighted rooted tree associated to ℤp 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.
  • Thumbnail Image
    Item
    A Value Region Problem for Continued Fractions and Discrete Dirac Equations
    (Project Euclid, 2020-06) Klimek, Slawomir; Mcbride, Matt; Rathnayake, Sumedha; Sakai, Kaoru; Mathematical Sciences, School of Science
    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.