# Vladyslav Elijovych Lyantse (in honour of the 100th anniversary of birth)

### Abstract

Some pages of biography and main scientific achievements of professor Wladyslaw Elijowich Lyantse, a famous mathematician, are presented.

### References

T. Kudryk, V. Lyantse, V. Neves, Nonstandard universe based on internal set theory, Functional analysis and its applications, North-Holland Math. Stud., 197 (2004), 155–166.

V. Lyantse, G. Chuyko, Rings of projectors and operator-valued measures, Spectral analysis and its applications, Theta Ser. Adv. Math., 2 (2003), 151–160.

V. Lyantse, T. Kudryk, About nearstandardness, Functional analysis, (Russian), Ulyanovsk. Gos. Ped. Univ., (2003), no. 38, 63–77.

V. Lyantse, T. Kudryk, On near-standardness in Hilbert spaces, Sibirsk. Mat. Zh., 43 (2002), no. 5,

–1094.

T. Kudryk, V. Lyantse, Standard filling of a product space, Mat. Stud., 16 (2001), no. 2, 169–184.

V. Lyantse, Shadow of a measure, Rend. Accad. Naz. Sci. XL Mem. Mat. Appl., 23 (1999), no. 5,

–123.

V. Lyantse, G. Chuyko, Some nonclassical problem of elasticity theory, Mat. Stud., 11 (1999), no. 2,

–188.

T. Banakh, V. Lyantse, Ya. Mykytyuk, ∞-convex sets and their applications to the proof of certain

classical theorems of functional analysis, Mat. Stud., 11 (1999), no. 1, 83—84.

V. Lyantse, Yu. Yavorsky, Nonstandard Sturm-Liouville difference operator, II, Mat. Stud., 11 (1999),

no. 1, 71–82.

V. Lyantse, Yu. Yavorsky, Nonstandard Sturm-Liouville difference operator, Mat. Stud., 10 (1998), no.

, 54–68.

V. Lyantse, Yu. Yavorsky, A nonstandard difference Sturm-Liouville operator, Bull. Polish Acad. Sci. Math., 46 (1998), no. 3, 285–290.

V. Lyantse, T. Kudryk, Introduction to nonstandard analysis, Mathematical Studies Monograph Series, 3 (1997), VNTL Publishers, Lviv, 255.

T. Kudryk, V. Lyantse, Operator-valued charges on finite sets, Mat. Stud., 7 (1997), no. 2, 145–156.

V. Lyantse, Nearstandardness on a finite set, Dissertationes Math. (Rozprawy Mat.), (1997), 369, 63.

T. Kudryk, V. Lyantse, G. Chuyko, Nearstandard operators, Mat. Stud., 3 (1994), 29–40, 120.

T. Kudryk, V. Lyantse, G. Chuyko, Nearstandardness on finite sets, Mathematical investigations (Ukrainian), Pr. Lviv. Mat. Tov., 2 (1993), 25–34, 107.

V. Lyantse, D. Potyagaylo, M. Fedyk, On a boundary value problem of conjugation, Mat. Metody i Fiz.-Mekh. Polya, 30 (1989), 20–24, 101.

V. Lyantse, The Stokes formula for functions of a discrete argument, Dokl. Akad. Nauk Ukrain. SSR, 6(1991), 16-19, 80.

V. Lyantse, O. Storozh, A nonclassical boundary value problem in the theory of plates, Dokl. Akad. Nauk Ukrain. SSR Ser. A 3 (1990), 15–17, 86.

T. Kudryk, V. Lyantse, Near-standardness, Methods for studying differential and integral operators (Russian), ”Naukova Dumka”, Kyiv, (1989), 116–121, 216.

V. Lyantse, On a perturbation that is infinitely small in the strong operator topology, Ukrain. Mat. Zh., 41 (1989), no. 7, 989–992, 1009.

V. Lyantse, G. Chuyko, A nonclassical boundary value problem in elasticity theory, Dokl. Akad. Nauk Ukrain. SSR Ser. A 2 (1989), 15–18, 85.

V. Lyantse, T. Kudryk, Functions of a discrete variable, Mathematics today ’88 (Russian), ”Vyshcha Shkola”, Kyiv, (1988), 132–139.

V. Lyantse, S. Pidkuyko, A nonclassical boundary value problem, Dokl. Akad. Nauk Ukrain. SSR Ser. A, 12 (1987), 14—16, 85.

V. Lyantse, M. Fedyk, Properties of operators generated by sesquilinear forms, Dokl. Akad. Nauk Ukrain. SSR Ser. A 2 (1987), 27—29, 87.

V. Lyantse, Nonstandard analysis, Mathematics today ’86 (Russian), ”Vyshcha Shkola”, Kyiv, 1986, 26–44.

V. Lyantse, O. Storozh, The resolvent of a perturbed operator, Mat. Metody i Fiz.-Mekh. Polya, 19 (1984), 23–25.

V.E. Lyantse, O.G. Storozh, Methods of the theory of unbounded operators, ”Naukova Dumka”, Kyiv, (1983), 221.

V. Lyantse, Is it possible to ignore nonstandard analysis? (Jordan form of an operator in an infinite-dimensional space), General theory of boundary value problems, ”Naukova Dumka”, Kyiv, (1983), 108–112.

V. Lyantse, Kh. Mayorga, On the theory of a one-point boundary value problem for the Laplace operator. II, Teor. Funktsii i Funktsional. Anal. i Prilozhen., (1983), no. 39, 87–94.

V. Lyantse, O. Storozh, Conditions for the coincidence of two operators, Visnyk Lviv. Derzh. Univ. Ser. Mekh.-Mat., (1982), no. 20, 14–17, 90.

V. Lyantse, O. Storozh, Some perturbation of linear operators with variation in their domain of definition, Mat. Metody i Fiz.-Mekh. Polya, (1982), no. 15, 25–30.

V. Lyantse, Kh. Mayorga, On the theory of a one-point boundary value problem for the Laplace operator. I, Teor. Funktsii i Funktsional. Anal. i Prilozhen.,(1982), no. 38, 84–91, 128–129.

V. Lyantse, O. Storozh, Operators that satisfy smoothness conditions, Ukrain. Mat. Zh., 34 (1982), no. 4, 451-455, 539.

V. Lyantse, O. Storozh Operators related to a selfadjoint operator, Visnyk Lviv. Derzh. Univ. Ser. Mekh.-Mat., (1981), no. 18, 42–45.

V. Lyantse, O. Storozh, A nonlocal boundary condition, Functional analysis, Ulyanovsk. Gos. Ped. Inst., (1981), no. 16, 59–66.

V. Lyantse, G. Chuyko, Operator measures, Dokl. Akad. Nauk Ukrain. SSR Ser. A(7), (1981), 7–9.

V. Lyantse, V. Kolesnyk, A condition for the correctness of a symbol of a one-dimensional pseudodifferential operator, Vestnik Lvov. Politekhn. Inst., (1980), no. 141, 52–53, 118.

V. Lyantse, Ya. Mykytyuk, The tensor product of linear operators, Mat. Metody i Fiz.-Mekh. Polya, (1980), no. 12, 88–89, 122.

V. Lyantse, O. Storozh, Mutual adjointness conditions for certain closed operators in terms of abstract boundary operators, Dokl. Akad. Nauk Ukrain. SSR Ser. A(6), (1980), 29–32, 92.

V. Lyantse, O. Storozh, Perturbation of a boundary operator, Visnik Lviv. Derzh. Univ. Ser. Mekh.-Mat., (1979), no. 14, 18–21.

V. Blashchak, V. Lyantse, The graph norm for a tensor product of linear operators, Visnyk Lviv. Politehn. Inst., (119 Mat. i Meh.), (1977), 11–13, 182.

V. Lyantse, Functionals of step functions, Visnyk Lviv. Politehn. Inst. (119 Mat. i Meh.), (1977), 165–167, 201.

V. Lyantse, A first order one-dimensional pseudodifferential operator with constant coefficients, Teor. Funkcii i Funkcional. Anal. i Prilovzen. (Vyp. 28), (1977), 64–84, iii.

V. Lyantse, The uniqueness of the generalized solution of the system of equations of gas dynamics, Dokl. Akad. Nauk SSSR, (1974), no. 215, 535–538.

V. Lyantse, Expansion in the eigenfunctions of a one-dimensional first order pseudodifferential operator with constant coefficients, Dokl. Akad. Nauk SSSR, (1973), no. 213, 38-41.

V. Lyantse, I. Syroid, The spectrality of the perturbed operator of multiplication by the independent variable, Mat. Zametki, (1973), no. 13, 289–296.

Yu. Kyshakevych, V. Lyantse, The radical of a certain normed ring, Visnyk Lviv. Derzh. Univ. Ser. Meh.-Mat., (1972), no. 7, 53–60, 133.

V. Lyantse, Closed operators in Hilbert space, Teor. Funkcii i Funkcional. Anal. i Prilozhen., (1972), no. 16, 165-186, 220.

V. Lyantse, On certain relations between closed operators, Dokl. Akad. Nauk SSSR, (1972), no. 204, 542–545.

V. Lyantse, Completely regular perturbation of a continuous spectrum. II, Mat. Sb. (N.S.), 84 (1971), no. 126, 141–158.

G. Keselman, V. Lyantse, The expansion in principal functions of a nonselfadjoint differential operator of order 2n with spectral singularities,Differencialnye Uravnenija, (1970), no. 6, 497–512.

V. Lyantse, Completely regular perturbation of a continuous spectrum, Mat. Sb. (N.S.), 82 (1970), no. 124, 126-156.

V. Lyantse, Eigen-element expansion of a nonselfadjoint difference operator, Ukrain. Mat. Zh., (1969), no. 21, 461–474.

V. Lyantse, The perturbation of a continuous spectrum, Dokl. Akad. Nauk SSSR,(1969), no. 187, 514–517.

V. Lyantse, Spectrum and resolvent of a nonselfadjoint difference operator, Ukrain. Mat. Zh.,(1968), no. 20, 489–503.

V. Lyantse, A nonselfadjoint one-dimensional perturbation of the operator of multiplication by the independent variable, Dokl. Akad. Nauk SSSR, (1968), no. 182, 1010–1013.

V. Lyantse, A non-selfadjoint difference operator, Dokl. Akad. Nauk SSSR, (1967), no. 173, 1260–1263.

V. Lyantse, An analog of the inverse problem of scattering theory for a non-selfadjoint operator, Mat. Sb. (N.S.), 72 (1967), no. 114, 537–557.

V. Lyantse, Expansion in principal functions of an operator with spectral singularities, Rev. Roumaine Math. Pures Appl. 11 (1966), 921–950; ibid., 11, 1187–1224.

V. Lyantse, The inverse problem for a nonselfadjoint operator, Dokl. Akad. Nauk SSSR, (1966), no. 166, 30–33.

V. Lyantse, On a differential operator with spectral singularities. II, Mat. Sb. (N.S.), 65 (1964), no. 107, 47–103.

V. Lyantse, On a differential operator with spectral singularities, I. Mat. Sb. (N.S.), 64 (1964), no. 106, 521–561.

V. Lyantse, Extension of the Fourier L-transform to locally square integrable functions, Dokl. Akad. Nauk SSSR (1964), no. 158, 1026–1029.

V. Lyantse, A non-selfadjoint differential operator of second order on a semi-axis, Dokl. Akad. Nauk SSSR (1964), no. 154, 1030–1033.

V. Lyantse, Unbounded operators commuting with the resolution of the identity, Ukrain. Mat. Zh., (1963), no. 15, 376–384.

V. Lyantse, The solution of certain boundary-value problems by the Fourier method, Dokl. Akad. Nauk SSSR, (1963), no. 152, 816–819.

V. Lyantse, Inversion formulas in the class of unbounded functions, arising in a second-order boundary-value problem, Dokl. Akad. Nauk SSSR, (1963), no. 150, 987—990.

V. Lyantse, The eigenfunction expansion of a non-selfadjoint differential operator with spectral singularities, Dokl. Akad. Nauk SSSR, (1963), no. 149, 256–259.

V. Lyantse, A generalization of the concept of spectral measure, Mat. Sb. (N.S.), 61 (1963), no. 103, 80–120.

V. Lyantse, A generalization of the concept of spectral operator, Dokl. Akad. Nauk SSSR, (1962), no. 142, 278-281.

V. Lyantse, Conditions for closedness of the contraction of a self-adjoint operator, Soviet Math. Dokl., (1960), no. 1, 709–712.

V. Lyantse, Certain properties of idempotent operators, Teoret. Prikl. Mat. Vyp., 1, (1958), 16–22.

V. Lyantse, Rings of unbounded operators based on a resolution of the identity and their representations, Dokl. Akad. Nauk SSSR, (1958), no. 121, 801–804.

V. Lyantse,. The integration of operator-valued functions with respect to a spectral measure, Lvov. Politekhn. Inst. Nauchn.Zap. Ser. Fiz.-Mat. Vyp., 38 (1956), 32-44.

V. Lyantse, On the theory of topological fields, Lvov. Politekhn. Inst. Nauchn. Ser. Fiz.-Mat. Vyp., 38 (1956), 29-31.

V. Lyantse, On a boundary problem for parabolic systems of differential equations with a strongly elliptic right-hand side, Mat. Sb. N.S., 35 (1954), no. 77, 357–368.

V. Lyantse, On differential equations in unitary space, Dopovidi Akad. Nauk Ukrain. RSR, (1952), 258–262.

V. Lyantse, On Cauchy’s problem in a domain of functions of real variables, Ukrain. Mat. Zhurnal,(1949), no. 4, 42–63.

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