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.
"A Value Region Problem for Continued Fractions and Discrete Dirac Equations." Hokkaido Math. J. 49 (2) 333 - 348, June 2020. https://doi.org/10.14492/hokmj/1602036029