Egor Maximenko, list of publications




  1. Grudsky, S.M.; Maximenko, E.A.; Soto-González, A. (2021):
    Eigenvalues of tridiagonal Hermitian Toeplitz matrices with perturbations in the off-diagonal corners.
    Chapter in the book: Karapetyants, A.N.; Kravchenko, V.V.; Liflyand, E.; Malonek H.R. (eds.) Operator Theory and Harmonic Analysis. OTHA 2020.
    Springer Proceedings in Mathematics & Statistics, vol. 357. Springer, Cham.
    ISBN 978-3-030-77492-9, e-ISBN 978-3-030-77493-6, DOI: 10.1007/978-3-030-77493-6_11.
    Preprint: arXiv:2009.01401 [math.FA].
  2. Leal-Pacheco, C.R.; Maximenko, E.A.; Ramos-Vazquez, G. (2021):
    Homogeneously polyanalytic kernels on the unit ball and the Siegel domain.
    Complex Anal. Oper. Theory 15, 99. DOI: 10.1007/s11785-021-01145-z.
  3. Barrera-Castelán, R.M.; Maximenko, E.A.; Ramos-Vazquez, G. (2021):
    Radial operators on polyanalytic weighted Bergman spaces.
    Bol. Soc. Mat. Mex. 27, 43. DOI: 10.1007/s40590-021-00348-w.
  4. Alexandersson, P.; González-Serrano, L.A.; Maximenko, E.A.; Moctezuma-Salazar, M.A. (2021):
    Symmetric polynomials in the symplectic alphabet and the change of variables zj = xj + xj−1.
    Electron. J. Comb. 28, issue 1, P1.56. DOI: 10.37236/9354 (open access).
    See also tests in Sagemath.
  5. Maximenko, E.A.; Tellería-Romero, A.M. (2020):
    Radial operators in polyanalytic Bargmann–Segal–Fock spaces.
    Chapter in the book: Bauer, W.; Duduchava, R.; Grudsky, S.; Kaashoek, M. (eds.) Operator Algebras, Toeplitz Operators and Related Topics, pp. 277–305.
    Book series Operator Theory: Advances and Applications, vol. 279. Birkhäuser, Cham.
    ISBN 978-3-030-44650-5, e-ISBN 978-3-030-44651-2, DOI: 10.1007/978-3-030-44651-2_18.
  6. Barrera, M.; Böttcher, A.; Grudsky, S.M.; Maximenko, E.A. (2018):
    Eigenvalues of even very nice Toeplitz matrices can be unexpectedly erratic.
    Chapter in the book: Böttcher, A.; Potts, D.; Stollmann, P.; Wenzel, D. (eds.) The Diversity and Beauty of Applied Operator Theory, pp. 51–77.
    Book series Operator Theory: Advances and Applications, vol. 268. Birkhäuser, Cham.
    DOI: 10.1007/978-3-319-75996-8_2.
  7. Böttcher, A.; Bogoya, J.M.; Grudskii, S.M.; Maximenko, E.A. (2017):
    Asymptotic formulas for the eigenvalues and eigenvectors of Toeplitz matrices.
    Sbornik: Mathematics, 208:11, 1578–1601. DOI: 10.1070/SM8865.
  8. Maximenko, E.A.; Moctezuma-Salazar, M.A. (2017):
    Cofactors and eigenvectors of banded Toeplitz matrices: Trench formulas via skew Schur polynomials.
    Operators and Matrices 11:4, 1149–1169. DOI: 10.7153/oam-2017-11-79 (open access).
    See also an interactive visualization of Toeplitz minors expressed via skew Schur polynomials.
  9. Bogoya, J.M.; Grudsky, S.M.; Maximenko, E.A. (2017):
    Eigenvalues of Hermitian Toeplitz matrices generated by simple-loop symbols with relaxed smoothness.
    Chapter in the book: Large Truncated Toeplitz Matrices, Toeplitz Operators, and Related Topics, pp. 179–212.
    Book series Operator Theory: Advances and Applications, vol. 259. Springer International Publishing.
    Print ISBN: 978-3-319-49180-6, Online ISBN: 978-3-319-49182-0, Series ISSN: 0255-0156. DOI: 10.1007/978-3-319-49182-0_11.
  10. Hutník, O.; Maximenko, E.A.; Mišková, A. (2016):
    Toeplitz localization operators: spectral functions density.
    Complex Anal. Oper. Theory, 10:8, 1757–1774. DOI: 10.1007/s11785-016-0564-1.
  11. Esmeral, K.; Maximenko, E.A. (2016):
    Radial Toeplitz operators on the Fock space and square-root-slowly oscillating sequences.
    Complex Anal. Oper. Theory, 10:7, 1655–1677. DOI: 10.1007/s11785-016-0557-0.
    See also a presentation.
  12. Bogoya, J.M.; Böttcher, A.; Maximenko, E.A. (2016):
    From convergence in distribution to uniform convergence.
    Boletín de la Sociedad Matemática Mexicana, 22:2, 695–710. DOI: 10.1007/s40590-016-0105-y.
    See also an an interactive illustration of the Lévy arcsine law turned inside out.
  13. Bogoya, J.M.; Böttcher, A.; Grudsky, S.M.; Maximenko, E.A. (2016):
    Eigenvectors of Hermitian Toeplitz matrices with smooth simple-loop symbols.
    Linear Algebra Appl., 493, 606–637. DOI: 10.1016/j.laa.2015.12.017.
    See also an interactive illustration of the eigenvalues and eigenvectors of Kac–Murdock–Szegő family of Toeplitz matrices.
  14. Esmeral, K.; Maximenko, E.A.; Vasilevski, N. (2015):
    C*-algebra generated by angular Toeplitz operators on the weighted Bergman spaces over the upper half-plane.
    Integr. Equ. Oper. Theory, 83:3, 413–428. DOI: 10.1007/s00020-015-2243-4.
    See a preprint on ResearchGate or here.
  15. Herrera Yañez, C.; Maximenko, E.A.; Vasilevski, N. (2015):
    Radial Toeplitz operators revisited: Discretization of the vertical case.
    Integr. Equ. Oper. Theory, 83:1, 49–60. DOI: 10.1007/s00020-014-2213-2.
    See a preprint on ResearchGate or here.
  16. Bogoya, J.M.; Böttcher, A.; Grudsky, S.M.; Maximenko, E.A. (2015):
    Maximum norm versions of the Szegő and Avram-Parter theorems for Toeplitz matrices.
    J. Approx. Theory, 196, 79–100. DOI: 10.1016/j.jat.2015.03.003.
    See also an interactive constructor of examples.
  17. Bogoya, J.M.; Böttcher, A.; Grudsky, S.M.; Maximenko, E.A. (2015):
    Eigenvalues of Hermitian Toeplitz matrices with smooth simple-loop symbols.
    J. Math. Anal. Appl., 422:2, 1308–1334. DOI: 10.1016/j.jmaa.2014.09.057.
  18. Esmeral, K.; Maximenko, E.A. (2014):
    C*-algebra of angular Toeplitz operators on Bergman spaces over the upper half-plane.
    Commun. Math. Anal., 17:2, 151–162. http://projecteuclid.org/euclid.cma/1418919761.
  19. Herrera Yañez, C.; Hutník, O.; Maximenko, E.A. (2014):
    Vertical symbols, Toeplitz operators on weighted Bergman spaces over the upper half-plane and very slowly oscillating functions.
    Comptes Rendus Mathematique, 352:2, 129–132. DOI: 10.1016/j.crma.2013.12.004.
  20. Herrera Yañez, C.; Maximenko, E.A.; Vasilevski, N. (2013):
    Vertical Toeplitz operators on the upper half-plane and very slowly oscillating functions.
    Integr. Equ. Oper. Theory, 77:2, 149–166. DOI: 10.1007/s00020-013-2081-1.
    See a preliminary version on ResearchGate or here.
  21. Grudsky, S.M.; Maximenko, E.A.; Vasilevski, N.L. (2013):
    Radial Toeplitz operators on the unit ball and slowly oscillating sequences.
    Commun. Math. Anal., 14:2, 77–94. http://projecteuclid.org/euclid.cma/1356039033.
    See a preprint on ResearchGate or here.
  22. Bogoya, J.M.; Böttcher, A.; Grudsky, S.M.; Maksimenko, E.A. (2012):
    Eigenvectors of Hessenberg Toeplitz matrices and a problem by Dai, Geary, and Kadanoff.
    Linear Algebra Appl., 436:9, 3480–3492. DOI: 10.1016/j.laa.2011.12.012 (open access).
  23. Böttcher, A; Grudsky, S.M.; Maksimenko, E.A. (2010):
    On the structure of the eigenvectors of large Hermitian Toeplitz band matrices.
    Chapter in the book: Recent Trends in Toeplitz and Pseudodifferential Operators, pp. 15–36.
    Book series Operator Theory: Advances and Applications, vol. 210. Springer Basel AG.
    Print ISBN: 978-3-0346-0547-2. Online ISBN: 978-3-0346-0548-9. Series ISSN: 0255-0156. DOI: 10.1007/978-3-0346-0548-9_2.
    Preprint: http://www.mathematik.tu-chemnitz.de/preprint/2009/PREPRINT_05.html
  24. Böttcher, A.; Grudsky, S.M.; Maksimenko, E.A. (2010):
    Inside the eigenvalues of certain Hermitian Toeplitz band matrices.
    J. Comput. Appl. Math., 233:9, 2245–2264. DOI: 10.1016/j.cam.2009.10.010 (open access).
  25. Böttcher, A.; Grudsky, S.M.; Maksimenko, E.A. (2009):
    On the asymptotics of all eigenvalues of Hermitian Toeplitz band matrices.
    Doklady Mathematics, 80:2, 662–664. DOI: 10.1134/S1064562409050081.
  26. Böttcher, A.; Grudsky, S.; Maksimenko, E.A.; Unterberger, J. (2009):
    The first order asymptotics of the extreme eigenvectors of certain Hermitian Toeplitz matrices.
    Integr. Equ. Oper. Theory, 63:2, 165–180. DOI: 10.1007/s00020-008-1646-x.
  27. Böttcher, A.; Grudsky, S.M.; Maksimenko, E.A. (2008):
    The Szegö and Avram-Parter theorems for general test functions.
    Comptes Rendus Mathematique, 346:13–14, 749–752. DOI: 10.1016/j.crma.2008.06.002.
  28. Böttcher, A.; Grudsky, S.M.; Maksimenko, E.A. (2008):
    Pushing the envelope of the test functions in the Szegö and Avram-Parter theorems.
    Linear Algebra Appl., 429:1, 346–366. DOI: 10.1016/j.laa.2008.02.031 (open access).
  29. Vasil'ev, V.A.; Maksimenko, E.A.; Simonenko, I.B. (2003):
    One Szegö-Widom limit theorem.
    Doklady Mathematics, 68:3, 361–362.
    See a draft version on ResearchGate or here.
  30. Maximenko, E.A. (2003):
    Convolution operators on expanding polyhedra: limits of the norms of inverse operators and pseudospectra.
    Sib. Math. J., 44:6, 1027–1038. DOI: 10.1023/B:SIMJ.0000007478.13348.97.
    See a draft version on ResearchGate or here.

See also MathSciNet, Scopus, Scholar Google, Research Gate, ORCID, Publons, and Math Genealogy.

In the Web of Knowledge please search by ResearchID = N-8833-2014.


Most of my recent investigations on the eigenvalues of Toeplitz matrices have been made jointly with

Most of my recent investigations on C*-algebras of operators in Reproducing Kernel Hilbert Spaces have been made jointly with


Return to my personal page or to the page of my courses in IPN-ESFM (in simple Spanish).