Murach Oleksandr Oleksandrovich
Publications
Research monograph
Mikhailets V. A., Murach A. A. Hormander Spaces, Interpolation, and Elliptic problems. De Gruyter, Berlin, 2014. xii+297 pp. https://doi.org/10.1515/9783110296891
More than 130 research papers. Among them are the following:
Mikhailets V., Murach A., Zinchenko T. An extended Hilbert scale and its applications. Advances in Mathematics, vol. 465 (2025), article no. 110155. https://doi.org/10.1016/j.aim.2025.110155
Mikhailets V., Murach A. Unconditional convergence of eigenfunction expansions for abstract and elliptic operators. Proceedings of the Royal Society of Edinburgh, Sect. A: Mathematics, 2024, First view. https://doi.org/10.1017/prm.2024.40
Mikhailets V., Murach A., Tsyhanok O. A new look at old theorems of Fejér and Hardy. Results in Mathematics, vol. 79 (2024), no. 2, article no. 88. https://doi.org/10.1007/s00025-023-02114-y
Los V., Mikhailets V., Murach A. Parabolic problems in generalized Sobolev spaces. Communications on Pure and Applied Analysis, 20 (2021), no. 10, 3589-3620. https://doi.org/10.3934/cpaa.2021123
Anop A., Denk R., Murach A. Elliptic problems with rough boundary data in generalized Sobolev spaces. Communications on Pure and Applied Analysis, 20 (2021), no. 2, 697-735. https://doi.org/10.3934/cpaa.2020286
Anop A., Chepurukhina I., Murach A. Elliptic problems with additional unknowns in boundary conditions and generalized Sobolev spaces. Axioms, 10 (2021), article no. 292, 23 pp. https://doi.org/10.3390/axioms10040292
Kasirenko T., Mikhailets V., Murach A. Sobolev-like Hilbert spaces induced by elliptic operators. Complex Analysis and Operator Theory, 13 (2019), no. 3, 1431-1440. https://doi.org/10.1007/s11785-018-00886-8
Anop A. V., Kasirenko T. M., Murach O. O. Irregular elliptic boundary-value problems and Hörmander spaces. Ukrainian Mathematical Journal, 70 (2018), no. 3, 341-361. https://doi.org/10.1007/s11253-018-1504-1
Los V. M., Mikhailets V. A., Murach A. A. An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. Communications on Pure and Applied Analysis, 16 (2017), no. 1, 69-97. https://doi.org/10.3934/cpaa.2017003
Murach A., Los V. Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces. Open Mathematics, 15 (2017), 57-76. https://doi.org/10.1515/math-2017-0008
Hnyp Ye. V., Mikhailets V. A., Murach A. A. Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces. Electronic Journal of Differential Equations, 2017, no. 81, 1-13. https://ejde.math.txstate.edu/Volumes/2017/81/hnyp.pdf
Mikhailets V. A., Murach A. A., Soldatov V. O. Continuity in a parameter of solutions to generic boundary-value problems. Electronic Journal of Qualitative Theory of Differential Equations, 2016, no. 87, 1-16. https://doi.org/10.14232/ejqtde.2016.1.87
Mikhailets V. A., Murach A. A. Interpolation Hilbert spaces between Sobolev spaces. Results in Mathematics, 67 (2015), no. 1-2, 135-152. https://doi.org/10.1007/s00025-014-0399-x
Mikhailets V. A., Murach A. A. The refined Sobolev scale, interpolation, and elliptic problems. Banach Journal of Mathematical Analysis, 6 (2012), no. 2, 211-281. https://doi.org/10.15352/bjma/1342210171
Mikhailets V. A., Murach A. A. Hormander Spaces, Interpolation, and Elliptic problems. De Gruyter, Berlin, 2014. xii+297 pp. https://doi.org/10.1515/9783110296891
More than 130 research papers. Among them are the following:
Mikhailets V., Murach A., Zinchenko T. An extended Hilbert scale and its applications. Advances in Mathematics, vol. 465 (2025), article no. 110155. https://doi.org/10.1016/j.aim.2025.110155
Mikhailets V., Murach A. Unconditional convergence of eigenfunction expansions for abstract and elliptic operators. Proceedings of the Royal Society of Edinburgh, Sect. A: Mathematics, 2024, First view. https://doi.org/10.1017/prm.2024.40
Mikhailets V., Murach A., Tsyhanok O. A new look at old theorems of Fejér and Hardy. Results in Mathematics, vol. 79 (2024), no. 2, article no. 88. https://doi.org/10.1007/s00025-023-02114-y
Los V., Mikhailets V., Murach A. Parabolic problems in generalized Sobolev spaces. Communications on Pure and Applied Analysis, 20 (2021), no. 10, 3589-3620. https://doi.org/10.3934/cpaa.2021123
Anop A., Denk R., Murach A. Elliptic problems with rough boundary data in generalized Sobolev spaces. Communications on Pure and Applied Analysis, 20 (2021), no. 2, 697-735. https://doi.org/10.3934/cpaa.2020286
Anop A., Chepurukhina I., Murach A. Elliptic problems with additional unknowns in boundary conditions and generalized Sobolev spaces. Axioms, 10 (2021), article no. 292, 23 pp. https://doi.org/10.3390/axioms10040292
Kasirenko T., Mikhailets V., Murach A. Sobolev-like Hilbert spaces induced by elliptic operators. Complex Analysis and Operator Theory, 13 (2019), no. 3, 1431-1440. https://doi.org/10.1007/s11785-018-00886-8
Anop A. V., Kasirenko T. M., Murach O. O. Irregular elliptic boundary-value problems and Hörmander spaces. Ukrainian Mathematical Journal, 70 (2018), no. 3, 341-361. https://doi.org/10.1007/s11253-018-1504-1
Los V. M., Mikhailets V. A., Murach A. A. An isomorphism theorem for parabolic problems in Hörmander spaces and its applications. Communications on Pure and Applied Analysis, 16 (2017), no. 1, 69-97. https://doi.org/10.3934/cpaa.2017003
Murach A., Los V. Isomorphism theorems for some parabolic initial-boundary value problems in Hörmander spaces. Open Mathematics, 15 (2017), 57-76. https://doi.org/10.1515/math-2017-0008
Hnyp Ye. V., Mikhailets V. A., Murach A. A. Parameter-dependent one-dimensional boundary-value problems in Sobolev spaces. Electronic Journal of Differential Equations, 2017, no. 81, 1-13. https://ejde.math.txstate.edu/Volumes/2017/81/hnyp.pdf
Mikhailets V. A., Murach A. A., Soldatov V. O. Continuity in a parameter of solutions to generic boundary-value problems. Electronic Journal of Qualitative Theory of Differential Equations, 2016, no. 87, 1-16. https://doi.org/10.14232/ejqtde.2016.1.87
Mikhailets V. A., Murach A. A. Interpolation Hilbert spaces between Sobolev spaces. Results in Mathematics, 67 (2015), no. 1-2, 135-152. https://doi.org/10.1007/s00025-014-0399-x
Mikhailets V. A., Murach A. A. The refined Sobolev scale, interpolation, and elliptic problems. Banach Journal of Mathematical Analysis, 6 (2012), no. 2, 211-281. https://doi.org/10.15352/bjma/1342210171