Publications

Published papers:

R.K., M.Vaktnäs, Szegő mapping and Hermite-Padé polynomials for multiple orthogonality on the unit circle, to appear in J. of Spectral Theory (2026), 27pp., under submission (arXiv:2601.04783).
R.K., M.Vaktnäs, Angelesco and AT systems on the Unit Circle, to appear in IMRN (2026), 21pp. (arXiv:2410.12094).
R.K., M.Vaktnäs, Determinantal Formulas for Rational Perturbations of Multiple Orthogonality Measures, J. of Approx. Theory, 318 (2026), https://doi.org/10.1016/j.jat.2026.106302, 36pp. (arXiv:2407.13961).
R.K., M.Vaktnäs, Zeros of multiple orthogonal polynomials: location and interlacing, Bull. of London Math. Soc. 58 (2026), no. 1, Paper No. e70281, 20 pp. (arXiv:2503.15122).
R.K., M.Vaktnäs, Christoffel Transform and Multiple Orthogonal Polynomials, J. Comput. Appl. Math. 476 (2026), Paper No. 117121, 26 pp. (arXiv:2407.13946).
G.Alpan, R.K., Multiplicative non-Hermitian perturbations of classical β-ensembles, Random Matrices Theory Appl. 14 (2025), no. 3, Paper No. 2550014, 22 pp. (arXiv:2308.06627).
R.K., M.Vaktnäs, Szegő recurrence for multiple orthogonal polynomials on the unit circle, Proc. of Amer. Math. Soc., 152, 7 (2024), pp.2983-2997 (arXiv:2404.18666).
R.K., M.Tyaglov, A generalized Hermite-Biehler theorem and non-Hermitian perturbations of Jacobi matrices, J. of Mathematical Analysis and Applications, Vol. 536(2) (2024), 128241 (arXiv:2302.07018).
R.K., Correction to: Jost asymptotics for matrix orthogonal polynomials on the real line, Constr. Approx. 58 (2023), no. 2, 545–549.
G.Alpan, R.K., Hermitian and non-Hermitian perturbations of chiral Gaussian β-ensembles, J. Math. Phys. 63, 043505 (2022) (arXiv:2109.13982).

M.Duits, B.Fahs, R.K., Global Fluctuations for Multiple Orthogonal Polynomial Ensembles, J. of Functional Analysis 281(5) (2021) (arXiv:1912.04599).
A.I.Aptekarev, R.K., Differential equations for the recurrence coefficients limits for multiple orthogonal polynomials from a Nevai class, J. Approx. Theory 255 (2020), 105409, 21 pp. (arXiv:1908.04540).
R.K., On Gaussian random matrices coupled to the discrete Laplacian, Oper. Theory Adv. Appl., 276 (2020), "Analysis as a Tool in Mathematical Physics", 434–447 (arXiv:1801.05749).
M.Duits, R.K., Relative Szegő asymptotics for Toeplitz determinants, IMRN, 2019(17) (2019), pp. 5441–5496, https://doi.org/10.1093/imrn/rnx266 (arXiv:1611.01020).
R.K., Rank one non-Hermitian perturbations of Hermitian β-ensembles of random matrices, J. of Statistical Phys. 168(1) (2017), pp. 92-108 (arXiv:1510.04456).
R.Killip, R.K., Matrix models and eigenvalue statistics for truncations of classical unitary ensembles of random matrices, Comm. Math. Phys. 349(3) (2017), pp 991-1027 (arXiv:1501.05160).
R.K., Finite range perturbations of finite gap Jacobi and CMV operators, Advances in Math. 301 (2016), pp 204-226 (arXiv:1410.7272).
R.K., Meromorphic continuations of finite gap Herglotz functions and periodic Jacobi matrices, Comm. Math. Phys. 327 (2014), no. 3, pp.921–950 (arXiv:1210.4627v2).
R.K., Jost asymptotics for matrix orthogonal polynomials on the real line, Constr. Approx. 36 (2012), no. 2, pp.267-309 (arXiv:1104.0460v2).
R.K., Equivalence classes of block Jacobi matrices, Proc. of Amer. Math. Soc., 139 (2011), pp.799-805 (arXiv:0911.1586v2).
R.K., Szegő asymptotics for matrix-valued measures with countably many bound states, J. of Approx. Theory, 162, Issue 6 (2010), pp.1211-1224 (arXiv:0910.1975v2).
R.K., L1-spectrum of Banach space valued Ornstein–Uhlenbeck operators, Semigroup Forum, Vol.78, no.3 (2009), pp.547-553 (arXiv:1210.1287).
R.K., Asymptotics of the eigenvalues of two-diagonal Jacobi matrices, Mathematical Notes, 77, no.1-2 (2005), pp.283-287 (arXiv:1210.1292).

Papers under submission:

R.K., M.Vaktnäs, Zeros of Laurent multiple orthogonal polynomials on the unit circle, 14pp., under submission (arXiv:2603.21468).
R.K., F.Štampach, Ratio asymptotics and zero density for orthogonal polynomials with varying Verblunsky coefficients, 32pp., under submission (arXiv:2511.22507).
R.K., Nikishin systems on the unit circle, 18pp., under submission (arXiv:2410.20813).
R.K., Spectral and resonance problem for perturbations of periodic Jacobi operators, 42pp, under submission (arXiv:1211.4274v3).

Papers in preparation:

R.Killip, R.K., Distribution of zeros of random orthogonal polynomials.