Egor Maximenko, list of publications




  1. Grudsky, S.M.; Maximenko, E.A.; Soto-González, A. (2022):
    Eigenvalues of the laplacian matrices of the cycles with one weighted edge.
    Linear Algebra Appl. 653, 86–115. DOI: 10.1016/j.laa.2022.07.011.
    See also an interactive illustration.
  2. Herrera-Yañez, C.; Maximenko, E.A.; Ramos-Vazquez, G. (2022):
    Translation-invariant operators in reproducing kernel Hilbert spaces.
    Integr. Equ. Oper. Theory 94, 31. DOI: 10.1007/s00020-022-02705-4.
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. Böttcher, A.; Bogoya, J.M.; Grudskii, S.M.; Maximenko, E.A. (2017):
    Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices.
    Sbornik: Mathematics, 208:11, 1578–1601. DOI: 10.1070/SM8865.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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).
  25. 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
  26. 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).
  27. 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.
  28. 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.
  29. 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.
  30. 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).
  31. 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.
  32. 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, WebOfScience, and Math Genealogy.


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).










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