Publications

31. M.D., Jeffrey S. Geronimo. The entries of a refinement equation and a generalization of the discrete wave equation. arXiv

30. M.D., Anastasiia Minenkova, Nathan Sun. A Theorem of Joseph-Alfred Serret and its Relation to Perfect Quantum State Transfer. arXiv

29. M.D., Gerald V. Dunne, Gamal Mograby, Alexander Teplyaev. Perfect quantum state transfer on diamond fractal graphs. arXiv

28. M.D., Brian Simanek. Asymptotics for polynomials orthogonal in an indefinite metric. J. Math. Anal. Appl. 460 (2018), no. 2, 777–793. arXiv

27. M.D. Jacobi matrices generated by ratios of hypergeometric functions. J. Difference Equ. Appl. 24 (2018), no. 2, 267–276. arXiv

26. M.D. A note on Wall’s modification of the Schur algorithm and linear pencils of Jacobi matrices. J. Approx. Theory 221 (2017), 1–21. arXiv

25. M.D., Brian Simanek. On Szegő’s theorem for a nonclassical case. J. Funct. Anal. 272 (2017), no. 6, 2487–2503. arXiv

24. Alexander I. Aptekarev, M.D., Hiroshi Miki, Walter Van Assche. Multidimensional Toda lattices: continuous and discrete time. SIGMA Symmetry Integrability Geom. Methods Appl. 12 (2016), Paper No. 054, 30 pp. arXiv

23. Alexander I. Aptekarev, M.D., Walter Van Assche. Discrete integrable systems generated by Hermite-Padé approximants. Nonlinearity 29 (2016), no. 5, 1487–1506. arXiv

22. M.D., Luca Perotti, Michał Wojtylak. Truncations of a class of pseudo-Hermitian tridiagonal matrices. J. Math. Anal. Appl. 438 (2016), no. 2, 738–758. arXiv

21. Alexander I. Aptekarev, M.D., Walter Van Assche. On 2D discrete Schrödinger operators associated with multiple orthogonal polynomials. J. Phys. A 48 (2015), no. 6, 065201, 16 pp. arXiv

20. M.D. Spectral theory of the G-symmetric tridiagonal matrices related to Stahl’s counterexample. J. Approx. Theory 191 (2015), 58–70. arXiv

19. M.D., Satoshi Tsujimoto, Luc Vinet, Alexei Zhedanov. Bannai-Ito polynomials and dressing chains. Proc. Amer. Math. Soc. 142 (2014), no. 12, 4191–4206. arXiv

18. M.D., Francisco Marcellán. A note on the Geronimus transformation and Sobolev orthogonal polynomials. Numer. Algorithms 67 (2014), no. 2, 271–287. arXiv

17. M.D., Juan Carlos García-Ardila, Francisco Marcellán. Multiple Geronimus transformations. Linear Algebra Appl. 454 (2014), 158–183. arXiv

16. M.D. On the relation between Darboux transformations and polynomial mappings. J. Approx. Theory 172 (2013), 4–22. arXiv

15. M.D., Luc Vinet, Alexei Zhedanov. CMV matrices and little and big −1 Jacobi polynomials. Constr. Approx. 36 (2012), no. 3, 513–535. arXiv

14. M.D., Olga Holtz, Sergey Khrushchev, Mikhail Tyaglov. Szegő’s theorem for matrix orthogonal polynomials. J. Approx. Theory 164 (2012), no. 9, 1238–1261. arXiv

13. M.D., Vladimir Derkach. Darboux transformations of Jacobi matrices and Padé approximation. Linear Algebra Appl. 435 (2011), no. 12, 3056–3084. arXiv

12. M.D. Inverse problems for periodic generalized Jacobi matrices. J. Math. Anal. Appl. 384 (2011), no. 2, 444–452. arXiv

11. M.D. The Jacobi matrices approach to Nevanlinna-Pick problems. J. Approx. Theory 163 (2011), no. 2, 117–142. arXiv

10. M.D., Vladimir Derkach. Convergence of diagonal Padé approximants for a class of definitizable functions. Recent advances in operator theory in Hilbert and Krein spaces, 97–124, Oper. Theory Adv. Appl., 198, Birkhäuser Verlag, Basel, 2010. arXiv

9. Bernhard Beckermann, M.D., Alexei Zhedanov. The linear pencil approach to rational interpolation. J. Approx. Theory 162 (2010), no. 6, 1322–1346. arXiv

8. M.D., Alexei Zhedanov. An operator approach to multipoint Padé approximations. J. Approx. Theory 157 (2009), no. 1, 70–88. arXiv

7. M.D. Generalized Jacobi operators in Krein spaces. J. Math. Anal. Appl. 349 (2009), no. 2, 568–582. arXiv


PhD DISSERTATION, 2008


6. M.D., Vladimir Derkach. On the convergence of Padé approximants of generalized Nevanlinna functions. (Russian) Tr. Mosk. Mat. Obs. 68 (2007), 133–182 ISBN: 978-5-382-00135-7 ; translation in Trans. Moscow Math. Soc. 2007, 119–162.

5. M.D. Borg-type theorems for generalized Jacobi matrices and trace formulas. Methods Funct. Anal. Topology 12 (2006), no. 3, 220–233.

4. M.D. Borg-type theorems for generalized Jacobi matrices. (Russian) Mat. Zametki 77 (2005), no. 4, 637-640; translation in Math. Notes 77 (2005), no. 3-4, 587–591.

3. M.D., Vladimir Derkach. Spectral problems for generalized Jacobi matrices. Linear Algebra Appl. 382 (2004), 1–24.

2. M.D. On the Schur algorithm for indefinite moment problem. Methods Funct. Anal. Topology 9 (2003), no. 2, 133–145.

1. M.D. On the Schur algorithm for indefinite moment problem. Spectral and evolution problems, Vol. 11 (Sevastopol, 2000), 106–109, Natl. Taurida Univ. “V. Vernadsky”, Simferopolʹ, 2001.