Papers

  1. V. V. Kravchenko, E. L. Shishkina and S. M. Torba. A Neumann series of Bessel functions representation for solutions of the radial Dirac system. arXiv:2008.05035, 10pp.
  2. N. Gutiérrez Jiménez and S. M. Torba. Analytic approximation of transmutation operators for one-dimensional stationary Dirac operators and applications to solution of initial value and spectral problems. arXiv:2006.04932, 31pp.
  3. V. V. Kravchenko and S. M. Torba. An improved Neumann series of Bessel functions representation for solutions of perturbed Bessel equations. arXiv:2005.10403, 35pp.
  4. I. V. Kravchenko, V. V. Kravchenko, S. M. Torba and J. C. Dias. Generalized exponential basis for efficient solving of homogeneous diffusion free boundary problems: Russian option pricing. arXiv:1808.08290, 26pp.
  5. V. V. Kravchenko and S. M. Torba. A direct method for solving inverse Sturm-Liouville problems. Inverse Problems, accepted. 32pp. Available at arXiv:2010.15275.
  6. V. V. Kravchenko, E. L. Shishkina and S. M. Torba. A transmutation operator method for solving the inverse quantum scattering problem. Inverse Problems, 36 (2020), 125007 (23pp).
  7. K. V. Khmelnytskaya, V. V. Kravchenko and S. M. Torba. Time-dependent one-dimensional electromagnetic wave propagation in inhomogeneous media: exact solution in terms of transmutations and Neumann series of Bessel functions. Lobachevskii Journal of Mathematics, 41 (2020), no. 5, 785--796.
  8. S. M. Torba and W. A. Zúñiga-Galindo. Non-Archimedean Coulomb gases. J. Math. Phys., 61 (2020), 013504, 16pp.
  9. N. Gutiérrez Jiménez and S. M. Torba. Spectral parameter power series representation for solutions of linear system of two first order differential equations. Appl. Math. Comput., 370 (2020), 124911, 13pp.
  10. I. V. Kravchenko, V. V. Kravchenko, S. M. Torba and J. C. Dias. Pricing double barrier options on homogeneous diffusions: a Neumann series of Bessel functions representation. Int. J. Theor. Appl. Finance, 22 (2019), No. 6, 1950030, 24pp.
  11. R. Castillo-Pérez, V. V. Kravchenko and S. M. Torba. A method for computation of scattering amplitudes and Green functions of whole axis problems. Math. Meth. Appl. Sci., 42 (2019), 5106-5117.
  12. I. V. Kravchenko, V. V. Kravchenko and S. M. Torba. Solution of parabolic free boundary problems using transmuted heat polynomials. Math. Meth. Appl. Sci., 42 (2019), 5094-5105.
  13. V. V. Kravchenko, S. M. Torba and J. Yu. Santana-Bejarano. Generalized wave polynomials and transmutations related to perturbed Bessel equations. Math. Meth. Appl. Sci., 42 (2019), 5008-5028.
  14. V. V. Kravchenko, R. M. Porter and S. M. Torba. Spectral parameter power series for arbitrary order linear differential equations. Math. Meth. Appl. Sci., 42 (2019), 4902-4908.
  15. K. V. Khmelnytskaya, V. V. Kravchenko and S. M. Torba. A representation of the transmutation kernels for the Schrödinger operator in terms of eigenfunctions and applications. Appl. Math. Comput., 353 (2019), 274-281.
  16. V. V. Kravchenko, E. L. Shishkina and S. M. Torba. On a series representation for integral kernels of transmutation operators for perturbed Bessel equations. Math. Notes, 104 (2018), 552-570.
  17. V. V. Kravchenko and S. M. Torba. A Neumann series of Bessel functions representation for solutions of Sturm-Liouville equations. Calcolo, 55 (2018), article 11, 23pp.
  18. R. Castillo-Pérez, V. V. Kravchenko and S. M. Torba. A Neumann series of Bessel functions representation for solutions of perturbed Bessel equations. Appl. Anal., 97 (2018), 677-704.
  19. K. V. Khmelnytskaya, V. V. Kravchenko and S. M. Torba. Transmutation operators: construction and applications. in Proceedings of the 17th International Conference on Computational and Mathematical Methods in Science and Engineering CMMSE-2017, 2017, 1198--1206, ISBN 978-84-617-8697-7.
  20. V. V. Kravchenko and S. M. Torba. Asymptotics with respect to the spectral parameter and Neumann series of Bessel functions for solutions of the one-dimensional Schrödinger equation. J. Math. Phys., 58 (2017), 122107 (10pp.).
  21. V. V. Kravchenko, L. J. Navarro and S. M. Torba. Representation of solutions to the one-dimensional Schrödinger equation in terms of Neumann series of Bessel functions. Appl. Math. Comput., 314 (2017), 173-192.
  22. V. V. Kravchenko, J. A. Otero and S. M. Torba. Analytic Approximation of Solutions of Parabolic Partial Differential Equations with Variable Coefficients. Adv. Math. Phys., (2017), article 2947275, (5pp.).
  23. V. V. Kravchenko and S. M. Torba. Analytic approximation of transmutation operators and related systems of functions. Bol. Soc. Mat. Mex., 22 (2016), 389-429.
  24. K. V. Khmelnytskaya, V. V. Kravchenko and S. M. Torba. Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations. J. Math. Phys., 57 (2016), 051503 (10pp.).
  25. V. V. Kravchenko, S. Morelos and S. M. Torba. Liouville transformation, analytic approximation of transmutation operators and solution of spectral problems. Appl. Math. Comput., 273 (2016), 321-336.
  26. V. V. Kravchenko, S. M. Torba and U. Velasco-García. Spectral parameter power series for polynomial pencils of Sturm-Liouville operators and Zakharov-Shabat systems. J. Math. Phys., 56 (2015), 073508 (20pp.).
  27. V. V. Kravchenko and S. M. Torba. Construction of transmutation operators and hyperbolic pseudoanalytic functions. Complex Anal. Oper. Theory, 9 (2015), 379-429.
  28. R. Castillo-Pérez, V. V. Kravchenko and S. M. Torba. Analysis of graded-index optical fibers by the spectral parameter power series method. J. Opt., 17 (2015), 025607 (9pp).
  29. V. V. Kravchenko and S. M. Torba. Analytic approximation of transmutation operators and applications to highly accurate solution of spectral problems. J. Comput. Appl. Math., 275 (2015), 1-26.
  30. V. V. Kravchenko and S. M. Torba. Modified spectral parameter power series representations for solutions of Sturm-Liouville equations and their applications. Appl. Math. Comput., 238 (2014), 82-105.
  31. R. Castillo-Pérez, V. V. Kravchenko and S. M. Torba. Spectral parameter power series for perturbed Bessel equations. Appl. Math. Comput., 220 (2013), 676-694.
  32. S. M. Torba and W. Zuniga-Galindo. Parabolic Type Equations and Markov Stochastic Processes on Adeles. J. Fourier Anal. Appl., 19 (2013), 792-835.
  33. K. V. Khmelnytskaya, V. V. Kravchenko, S. M. Torba and S. Tremblay. Wave polynomials, transmutations and Cauchy’s problem for the Klein-Gordon equation. J. Math. Anal. Appl., 399 (2013), no. 1, 191-212.
  34. V. V. Kravchenko and S. M. Torba. Transmutations and spectral parameter power series in eigenvalue problems. Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. The Vladimir Rabinovich Anniversary Volume in Operator Theory: Advances and Applications, Vol. 228, 2013, 209-238.
  35. V. V. Kravchenko and S. M. Torba. Spectral problems in inhomogeneous media, spectral parameter power series and transmutation operators, in 2012 International Conference on Mathematical Methods in Electromagnetic Theory (MMET), IEEE Conference Publications 2012, p.18-22.
  36. V. V. Kravchenko, S. M. Torba. Transmutations for Darboux transformed operators with applications. J. Phys. A: Math. Theor. 45 (2012), 075201 (21pp).
  37. H. M. Campos, V. V. Kravchenko, S. M. Torba. Transmutations, L-bases and complete families of soutions of the stationary Schrodinger equation in the plane. J. Math. Anal. Appl. 389 (2012), no. 2, 1222-1238.
  38. S. Torba. Inverse theorems in the theory of approximation of vectors in a Banach space with exponential type entire vectors. Methods Funct. Anal. Topology 16 (2010), no. 1, pp. 69-82.
  39. Ya. Grushka, S. Torba. Direct and Inverse Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors. Operator Theory: Advances and Applications, Vol. 190 (2009), pp. 295-314.
  40. S. M. Torba and O. I. Kashpirovskyi. Characterization of the rate of convergence of one approximate method for the solution of an abstract Cauchy problem. Ukr.Math.J., Vol. 60, No. 4 (2008), pp.639-647.
  41. S. Albeverio, S. Kuzhel, S. Torba. p-Adic Schr ödinger-type operator with point interactions. J.Math.Anal.Appl. 338 (2008), vol.2, 1267–1281.
  42. Ya. Grushka, S. Torba. Direct theorems in the theory of approximation of Banach space vectors by exponential type entire vectors. Methods Funct. Anal. Topology 12 (2007), no. 3, 267–278.
  43. S. Torba. Direct and inverse theorems of approximate methods for the solution of an abstract Cauchy problem. Ukr.Math.J., 59 (2007), no. 6, 919–937.
  44. S. Kuzhel and S. Torba. p-adic fractional differentiation operator with point interactions. Methods Funct. Anal. Topology 13 (2007), no. 2, pp. 169–180.
  45. M. L. Horbachuk, Ya. I. Hrushka, and S. M. Torba. Direct and inverse theorems in the theory of approximation by the Ritz method. Ukr.Math.J., 57 (2005), no. 5, 751–764.
  46. M. L. Horbachuk, Ya. I. Hrushka, and S. M. Torba. Direct and inverse theorems in the theory of approximation in the Hilbert space. Dop.Nat.Acad.Nauk, 57 (2004), no. 9, 20–25.
  47. M.L. Gorbachuk and S.M. Torba. On existence of boundary values of polyharmonic functions. Methods Funct. Anal. Topology 10 (2004), no. 2, pp. 4–12.