Микитюк Ярослав Володимирович

Посада: завідувач кафедри математичного і функціонального аналізу

Науковий ступінь: кандидат фізико-математичних наук

Вчене звання: доцент

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Наукові інтереси

Функціональний аналіз, теорія операторів, обернені спектральні задачі, теорія розсіяння.

Публікації

[1] (with S. Albeverio and R. O. Hryniv) Inverse scattering for impedance Schr odinger operators, I. Step-like
impedans lattice, J. Math. Analysis and Appl., Auqust 2017, doi:10.1016/j.jmaa. 2017.07.068 (27 pp.)
[2] (with R. O. Hryniv) Eigenvalue asymptotics for Dirac–Bessel operators J. Math. Phys., 57, 2016, pp.
063507 (2016); http://dx.doi.org/10.1063/1.4953245.
[3] (with D. V. Puyda) On the accelerants of non-self-adjoint Dirac operators, Methods Funct. Anal. and
Topology, vol.20, no.4, 2014, pp. 349-364.
[4] (with D. V. Puyda) Bari–Markus property for Dirac operators, Mat. Stud., Vol.40, N 2, 2013, pp. 165-171.
[5] (with S. Albeverio, R. O. Hryniv and P. A. Perry) Inverse scattering for non-classical impedance Schr odinger
operators, Operator Theory: Advances and applications, Vol. 227, 1-42, 2013 Springer Basel AG
[6] (with R. O. Hryniv) Self-adjointness of Schr odinger operators with singular potentials Methods Funct.
Anal. Topology, vol.18, no.2, 2012, pp. 152-159.

[7] (with D. V. Puyda) Inverse spectral problems for Dirac operators on a finite interval, Journal of Mathemati-
cal Analysis and Applications, 386 (2012) pp. 177–194.

[8] (with S. Albeverio and R. O. Hryniv) Scattering theory for Schr odinger operators with Bessel-type potenti-
als, J. reine angew. Math., 666 (2012), 83-113.

[9] (with S. Albeverio and R. O. Hryniv) Inverse scattering for discontinuous impedance Schr odinger operators:
a model example, Journal of Physics A , 44 (2011) 345204.
[10] (with R. O. Hryniv and P.A. Perry) Inverse scattering on the line for Schrodinger operators with Miura
potentials, II. Different Riccati representatives, Comm. Partial Diff. Equat. 36 (2011), no.9, 1987-1623.
[11] (with N.S. Trush) Inverse spectral problems for Sturm–Liouville operators with matrix-valued potentials
Inverse Problems 26 (2010), 015009 (36pp).
[12] (with R. O. Hryniv) Asymptotics of zeros of some entire functions, Trans. AMS, 361 (2009), no. 4, 2207–
2223.
[13] (with S. Albeverio and R. O. Hryniv) Factorisation of non-negative Fredholm operators and inverse spectral
problems for Bessel operators, Integr.equ. oper. theory, 64 (2009), 301–323.
[14] (with C. Frayer, R. O. Hryniv and P.A. Perry) Inverse scattering for Schr odinger operators with Miura
potentials: I. Unique Riccati representatives and ZS-AKNS systems Inverse Problems 25 (2009), 115007
(25pp).
[15] (with S. Albeverio and R. O. Hryniv) On spectra of non-self-adjoint Sturm–Liouville operators, Sel. math.,
New ser. 13 (2008), no. 4, 571-599.
[16] (with S. Albeverio and R. O. Hryniv) Reconstruction of radial Dirac and Schr odinger operators from two
spectra, J. Math. Anal. Appl. 399 (2008), no. 1, 45–57.
[17] (with S. Albeverio and R. O. Hryniv) Inverse spectral problems for Bessel operators, J. Diff. Equat. 241
(2007), no. 1, 130–159.
[18] (with N. Trush) Асимптотика нулiв цiлих функцiй типу синус, що дiють у банаховiй алгебрi, Вiсник
НТШ. – Т.4 (2007).- С. 214-219.
[19] (with S. Albeverio, P. Binding, and R. O. Hryniv) Inverse spectral problems for compound oscillating
systems, Inverse Problems 23 (2007), 1181–1200.
[20] (with S. Albeverio and R. O. Hryniv) Reconstruction of radial Dirac operators, J. Math. Phys. 48 (2007),
no. 4, 043501 (14 p.)
[21] (with S. Albeverio and R. O. Hryniv) Inverse spectral problems for compound oscillating systems:
Reconstruction from three spectra, Meth. Funct. Anal. Topol. 13 (2007), no. 2, 110–123.
[22] (with R. O. Hryniv) Eigenvalue asymptotics for Sturm-Liouville operators with singular potentials, J.
Funct. Anal. 238 (2006), no. 1, 27–57.
[23] (with R. O. Hryniv) Inverse spectral problems for Sturm-Liouville operators with singular potentials, IV.
Potentials in the Sobolev space scale, Proc. Edinb. Math. Soc. 49 (2006), no. 2, 309–329.
[24] (with S. Albeverio and R. O. Hryniv) Inverse spectral problems for Sturm–Liouville operators in impedance
form, J. Funct. Anal. 222 (2005), 143–177.

[25] (with S. Albeverio and R. O. Hryniv) Inverse spectral problems for Dirac operators with summable potenti-
als, Russian J. Math. Phys. 12 (2005) no. 4, 406–423.

[26] (with R. O. Hryniv) Half–inverse problems for Sturm-Liouville operators with singular potentials, Inverse
Problems 20(2004), 1423–1444.
[27] (with R. O. Hryniv) Inverse spectral problems for Sturm-Liouville operators with singular potentials, II.
Reconstruction by two spectra, in Functional Analysis and its Applications, V. Kadets and W. Zelazko,
eds., North-Holland Mathematics Studies 197, 97–114, North-Holland Publishing Co., Amsterdam, 2004.
[28] (with R. O. Hryniv) Transformation operators for Sturm-Liouville operators with singular potentials, Math.
Phys. Anal. Geom. 7(2004), no. 2, 119–149.
[29] Факторизацiя фредгольмових операторiв в операторних алгебрах, Мат. Студ. 21 (2004), no. 1, 87–97.
[30] (with R. O. Hryniv) Inverse spectral problems for Sturm-Liouville operators with singular potentials, III.
Reconstruction by three spectra, J. Math. Anal. Appl. 284(2003), no. 2, 626–646.
[31] (with R. O. Hryniv) Inverse spectral problems for Sturm-Liouville operators with singular potentials,
Inverse Problems 19(2003), 665–684.
[32] (with A.K.Prykarpatsky and D.L. Blackmore) The Lax solution to the Hamilton-Jacobi equation and its
generalizations. II, Nonlinear Anal. 55(2003), no. 5, 629–640.
[33] (with J. Janas and D.L. M. Malejki) Similarity and the point spectrum of some non-selfadjoint Jacobi
matrices, Proc. Edinburgh Math. Soc. 46 (2003), 575–595.
[34] Ya.V. Mykytyuk, Factorization of Fredholm operators, (in Ukrainian) Mat. Stud. 20 (2003), no. 2, 185–199.
[35] R. O. Hryniv, Ya. V. Mykytyuk, Schr odinger operators with singular Gordon potentials, (English) Methods
of Functional Analysis and Topology 8 (2002), no.1, 36–48.
[36] R. O. Hryniv, Ya. V. Mykytyuk, Schr odinger operators with periodic singular potentials, (English) Methods
of Functional Analysis and Topology 7 (2001), no.4, 31–42.
[37] R. O. Hryniv, Ya. V. Mykytyuk, On similarity of pertubed multiplication operators, (Russian) Math.
Zametki 69 (2000), no.4, 74–81; Engl. transl.: Math. Notes 70 (2001), no. 1, 35–41.
[38] Ya. V. Mykytyuk, O. M. Sumyk, M. M. Sheremeta, On Young conjugate functions and the behavior of
the maximal terms of the derivatives of Dirichlet series, (Russian), Mat. Zametki 69 (2001), no. 1, 74–81;
Engl. transl.: Math. Notes 69 (2001), no. 1-2, 65–71.
[39] Yu. S. Dzhala, Ya. V. Mykytyuk, On the spectrum of a boundary problem for the biharmonic equation in
halfspace, (in Ukrainian) Nonlinear oscillation 3 (2000), no. 1, 44–48.
[40] Ya. V. Vasyl’kiv, Ya. V. Mykytyuk, Criteria for the boundedness of integral means of logarithms of Blaschke
products, (in Ukrainian) Dopov. Nats. Akad. Nauk Ukr. Mat. Prirodozn. Tekh. Nauki (2000), no. 8, 10–14.
[41] Ya.V. Mykytyuk, S.I. Fedynyak, M.M. Sheremeta, Dirichlet series of bounded l−M-index, (in Ukrainian)
Mat. Stud. 11 (1999), no. 2, 159–166.
[42] T. Banakh, W.E. Lyantse, Ya.V. Mykytyuk ∞-convex sets and their applications to the proof of certain
classical theorems of functional analysis, (English) Mat. Stud. 11 (1999), no. 1, 83–84.
[43] Yu.S. Dzhala, Ya.V. Mykytyuk, Singular perturbations of closed operators, (in Ukrainian) Mat. Stud. 11
(1999), no. 1, 53–62.
[44] Ya.V. Mykytyuk, M.I. Nagnibida, On the equivalence of some Pommiez operators in spaces of analytic
functions, (in Ukrainian) Mat. Stud. 9 (1998), no. 2, 193–198.
[45] Yu.S. Dzhala, Ya. V. Mykytyuk, Singular perturbations of selfadjoint operators, (in Ukrainian) Mat. Metodi
Fiz.-Mekh. Polya 41 (1998), no. 4, 46–54.
[46] Ya.V. Mykytyuk, S. I. Tarasyuk, On sequences of compact operators, (in Ukrainian) Mat. Stud. 8 (1997),
no.1, 111–112.
[47] Ya.V. Mykytyuk, T.I. Oleksiv, On the similarity of operators, (in Ukrainian) Mat. Stud. 5 (1995), 43–52.
[48] Ya.V. Mykytyuk, M. Al-Tundzhi, On the operator of multiplication by a matrix polynomial, (in Ukrainian)
Ukr. Mat. Zh. 44 (1992), no. 9, 1287–1289.
[49] Ya.V. Mykytyuk On a problem in integral geometry, (Russian) Teor. Funktsi ıFunktsional. Anal. i Prilozhen.
(1990), 53, 95–99.
[50] O.V. Dika, Ya.V. Mykytyuk Perturbation of the two-sided shift operator, (Ukrainian) Visnyk Lviv. Derzh.
Univ. Ser. Mekh.-Mat. 34, (1990), 50–51.
[51] Ya.V Mykytyuk, The singular spectrum of selfadjoint operators, (Russian) Dokl. Acad. Nauk SSSR 303
(1988), no. 1, 33–36. Engl. transl.: Soviet Math. Dokl. 38 (1989), no. 3, 472–475.
[52] Ya.V. Mykytyuk, Uniqueness theorems for analytic operator functions with a nonnegative imaginary part,
(Russian) Funktsional. Anal. i Prilozhen. 22 (1988), no. 1, 73–74. Engl. transl.: Functional Anal. Appl. 22
(1988), no. 1, 62–64.
[53] Ya.V. Mykytyuk, Discrete spectrum of a weakly perturbed multiplication operator, (in Ukrainian) Visnyk
Lviv. Derzh. Univ. Ser. Mekh.-Mat. 28, (1987), 41–43.
[54] Ya.V. Mykytyuk, Properties of a unitary operator, (in Ukrainian) Visnyk Lviv. Derzh. Univ. Ser. Mekh.-
Mat. 25, (1986), 41–42.

[55] Ya.V. Mykytyuk, Spectral properties of an elliptic operator, (Ukrainian) Visnyk Lviv. Derzh. Univ. Ser.
Mekh.-Mat. 21, (1983), 8–10.
[56] Ya.V. Mykytyuk, Differential operators on the axis with a boundary condition at zero, (Russian) Ukrain.
Mat. Zh. 34 (1982), no. 2, 219–222.
[57] Ya. V. Mykytyuk, Weakly regular perturbation, (Ukrainian) Visnyk Lviv. Derzh. Univ. Ser. Mekh.-Mat.
18, (1981), 45–49.
[58] Ya.V. Mykytyuk, Properties of a class of nonselfadjoint operators, (Russian) Funktsional. Anal. i Prilozhen.
15 (1981), no. 4, 85–86.
[59] Ya.V. Mykytyuk, Properties of certain singular integral operators, (in Ukrainian) Visnyk Lviv. Derzh. Univ.
Ser. Mekh.-Mat. 18, (1981), 50–53.
[60] V.E. Lyantse, Ya.V. Mykytyuk, The tensor product of linear operators, (Russian) Mat. Metody Fiz.-Mekh.
Polya 12 (1980) 88–89.
[61] Ya.V. Mykytyuk, Spectral theory of a class of nonselfadjoint operators, (Russian) Dokl. Acad. Nauk SSSR
252 (1980), no. 1, 40–43. Engl. transl.: Soviet Math. Dokl. 32(1981), no. 1, 272–276.
[62] Ya.V. Mykytyuk, On perturbation of continuous spectrum, (in Ukrainian) Visnyk Lviv. Politekh. Inst. 119,
(1977), 170–172.

Біографія

Народився 29 травня 1953 року. 1970 -1975 — роки навчання на механіко-математичному факультеті Львівського національного університету ім. Івана Франка. 1975-1978 — навчання в аспірантурі ЛНУ під керівництвом проф. Лянце В.Е. В 1982 році захистив кандидатську дисертацію на тему : “Оператори зі спектральними особливостями” З грудня 1978 року працював на посаді асистента кафедри теорії функцій та функціонального аналізу, а з лютого 1985 р. — доцент кафедри ТФФА. З липня 2016 року — завідувач каф. математичного та функціонального аналізу.

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