2018
Том 70
№ 6

All Issues

Berezansky Yu. M.

Articles: 58
Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 80th birthday)

Antoniouk A. Vict., Berezansky Yu. M., Boichuk A. A., Gutlyanskii V. Ya., Khruslov E. Ya., Kochubei A. N., Korolyuk V. S., Kushnir R. M., Lukovsky I. O., Makarov V. L., Marchenko V. O., Nikitin A. G., Parasyuk I. O., Pastur L. A., Perestyuk N. A., Portenko N. I., Ronto M. I., Sharkovsky O. M., Tkachenko V. I., Trofimchuk S. I.

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Ukr. Mat. Zh. - 2018. - 70, № 1. - pp. 3-6

Anniversaries (Ukrainian)

On the 100th birthday of outstanding mathematician and mechanic Yurii Oleksiiovych Mytropol’s’kyi (03.01.1917 – 14.06.2008)

Berezansky Yu. M., Boichuk A. A., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Parasyuk I. O., Perestyuk N. A., Samoilenko A. M., Sharkovsky O. M.

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Ukr. Mat. Zh. - 2017. - 69, № 1. - pp. 132-144

Anniversaries (Ukrainian)

Yurii Stephanovych Samoilenko (on his 70th birthday)

Berezansky Yu. M., Boichuk A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Nizhnik L. P., Samoilenko A. M., Sharko V. V., Sharkovsky O. M., Trohimchuk Yu. Yu

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Ukr. Mat. Zh. - 2013. - 65, № 10. - pp. 1408-1409

Anniversaries (Ukrainian)

Myroslav L’vovych Horbachuk (on his 75 th birthday)

Berezansky Yu. M., Gerasimenko V. I., Khruslov E. Ya., Kochubei A. N., Mikhailets V. A., Nizhnik L. P., Samoilenko A. M., Samoilenko Yu. S.

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Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 451-454

Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 75th birthday)

Berezansky Yu. M., Boichuk A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Nikitin A. G., Perestyuk N. A., Portenko N. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M., Trohimchuk Yu. Yu

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Ukr. Mat. Zh. - 2013. - 65, № 1. - pp. 3 - 6

Anniversaries (Ukrainian)

Yuri Yurievich Trokhimchuk (on his 80th birthday)

Berezansky Yu. M., Bojarski B., Gorbachuk M. L., Kopilov A. P., Korolyuk V. S., Lukovsky I. O., Mitropolskiy Yu. A., Portenko N. I., Reshetnyak Yu. G., Samoilenko A. M., Sharko V. V., Shevchuk I. A., Skorokhod A. V., Tamrazov P. M., Zelinskii Yu. B.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 5. - pp. 701 – 703

Article (Ukrainian)

Myroslav L’vovych Horbachuk (on his 70th birthday)

Adamyan V. M., Berezansky Yu. M., Khruslov E. Ya., Kochubei A. N., Kuzhel' S. A., Marchenko V. O., Mikhailets V. A., Nizhnik L. P., Ptashnik B. I., Rofe-Beketov F. S., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 439–442

Article (English)

Integration of a modified double-infinite Toda lattice by using the inverse spectral problem

Berezansky Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2008. - 60, № 4. - pp. 453–469

An approach to finding a solution of the Cauchy problem for a modified double-infinite Toda lattice by using the inverse spectral problem is given.

Anniversaries (Ukrainian)

Fifty years devoted to science (on the 70th birthday of Anatolii Mykhailovych Samoilenko)

Berezansky Yu. M., Dorogovtsev A. A., Drozd Yu. A., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Makarov V. L., Mitropolskiy Yu. A., Perestyuk N. A., Rebenko A. L., Ronto A. M., Ronto M. I., Samoilenko Yu. S., Sharko V. V., Sharkovsky O. M.

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Ukr. Mat. Zh. - 2008. - 60, № 1. - pp. 3–7

Anniversaries (Ukrainian)

Leonіd Andrіyovich Pastur (on his 70th birthday)

Baryakhtar V. G., Berezansky Yu. M., Khruslov E. Ya., Korolyuk V. S., Marchenko V. O., Mitropolskiy Yu. A., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 12. - pp. 1699-1700

Article (English)

Spectral theory and Wiener-Itô decomposition for the image of a Jacobi field

Berezansky Yu. M., Pulemyotov A. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 744–763

Assume that $K^+: H_- \rightarrow T_-$ is a bounded operator, where $H_—$ and $T_—$ are Hilbert spaces and $p$ is a measure on the space $H_—$. Denote by $\rho_K$ the image of the measure $\rho$ under $K^+$. This paper aims to study the measure $\rho_K$ assuming $\rho$ to be the spectral measure of a Jacobi field. We obtain a family of operators whose spectral measure equals $\rho_K$. We also obtain an analogue of the Wiener – Ito decomposition for $\rho_K$. Finally, we illustrate the results obtained by carrying out the explicit calculations for the case, where $\rho_K$is a Levy noise measure.

Anniversaries (Ukrainian)

Mark Grigorievich Krein (to the centenary of his birth)

Adamyan V. M., Arov D. Z., Berezansky Yu. M., Gorbachuk M. L., Gorbachuk V. I., Mikhailets V. A., Samoilenko A. M.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 5. - pp. 579-587

Article (English)

A generalization of an extended stochastic integral

Berezansky Yu. M., Tesko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 5. - pp. 588–617

We propose a generalization of an extended stochastic integral to the case of integration with respect to a broad class of random processes. In particular, we obtain conditions for the coincidence of the considered integral with the classical Itô stochastic integral.

Anniversaries (Ukrainian)

Evgen Yakovich Khruslov (on his 75 th birthday)

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Lukovsky I. O., Marchenko V. O., Mitropolskiy Yu. A., Nizhnik L. P., Pastur L. A., Samoilenko A. M., Sharko V. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 4. - pp. 549-550

Anniversaries (Ukrainian)

On the 90th birthday of Yurii Alekseevich Mitropol’skii

Berezansky Yu. M., Gorbachuk M. L., Korolyuk V. S., Koshlyakov V. N., Lukovsky I. O., Makarov V. L., Perestyuk N. A., Samoilenko A. M., Samoilenko Yu. I., Sharko V. V., Sharkovsky O. M., Stepanets O. I., Tamrazov P. M., Trohimchuk Yu. Yu

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Ukr. Mat. Zh. - 2007. - 59, № 2. - pp. 147–151

Anniversaries (Ukrainian)

Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

Berezansky Yu. M., Gorbachuk M. L., Gorbachuk V. I., Khruslov E. Ya., Kostyuchenko A. G., Kuzhel' S. A., Marchenko V. O., Samoilenko A. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 8. - pp. 1120-1122

Article (Ukrainian)

Functional Analysis in the Institute of Mathematics of the National Academy of Sciences of Ukraine

Berezansky Yu. M., Gorbachuk M. L., Gorbachuk V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 582–600

We give a brief survey of results on functional analysis obtained at the Institute of Mathematics of the Ukrainian National Academy of Sciences from the day of its foundation.

Article (Ukrainian)

Orthogonal Approach to the Construction of the Theory of Generalized Functions of Infinitely Many Variables and the Poisson Analysis of White Noise

Berezansky Yu. M., Tesko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 12. - pp. 1587-1615

We develop an orthogonal approach to the construction of the theory of generalized functions of infinitely many variables (without using Jacobi fields) and apply it to the construction and investigation of the Poisson analysis of white noise.

Article (Ukrainian)

Spaces of Test and Generalized Functions Related to Generalized Translation Operators

Berezansky Yu. M., Tesko V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 12. - pp. 1587-1657

We present main recent results on the generalization of white-noise analysis related to a family of generalized translation operators.

Brief Communications (English)

The Jacobi Field of a Lévy Process

Berezansky Yu. M., Lytvynov E. V., Mierzejewski D. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 5. - pp. 706-710

We derive an explicit formula for the Jacobi field that is acting in an extended Fock space and corresponds to an ( \(\mathbb{R}\) -valued) Lévy process on a Riemannian manifold. The support of the measure of jumps in the Lévy–Khintchine representation for the Lévy process is supposed to have an infinite number of points. We characterize the gamma, Pascal, and Meixner processes as the only Lévy process whose Jacobi field leaves the set of finite continuous elements of the extended Fock space invariant.

Anniversaries (Ukrainian)

Mykola Ivanovych Shkil' (On His 70th Birthday)

Berezansky Yu. M., Korolyuk V. S., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V.

Full text (.pdf)

Ukr. Mat. Zh. - 2002. - 54, № 12. - pp. 1589-1591

Anniversaries (Ukrainian)

Igor Volodymyrovych Skrypnik (On His 60th Birthday)

Berezansky Yu. M., Kharlamov P. V., Khruslov E. Ya., Kit G. S., Korneichuk N. P., Korolyuk V. S., Kovalev A. M., Kovalevskii A. A., Lukovsky I. O., Mitropolskiy Yu. A., Samoilenko A. M., Savchenko O. Ya.

Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1443-1445

Article (English)

On the Theory of Generalized Toeplitz Kernels

Berezansky Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2000. - 52, № 11. - pp. 1458-1472

A new proof of the integral representation of the generalized Toeplitz kernels is given. This proof is based on the spectral theory of the corresponding differential operator that acts in the Hilbert space constructed from a kernel of this sort. A theorem on conditions that should be imposed on the kernel to guarantee the self-adjointness of the operator considered (i.e., the uniqueness of the measure in the representation) is proved.

Article (Russian)

Stabilization for a finite time in problems with free boundary for some classes of nonlinear second-order equations

Berezansky Yu. M., Mitropolskiy Yu. A., Shkhanukov-Lafishev M. Kh.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 214–223

We obtain estimates for the time of stabilization of solutions of problems with free boundary for one-dimensional quasilinear parabolic equations.

Anniversaries (Ukrainian)

Yurii L’vovich Daletskii

Berezansky Yu. M., Korolyuk V. S., Krein S. G., Mitropolskiy Yu. A., Samoilenko A. M., Skorokhod A. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 323–325

Article (Ukrainian)

Infinite-dimensional analysis related to generalized translation operators

Berezansky Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 3. - pp. 364–409

We give an extensive generalization of the white-noise analysis (in the Gaussian and non-Gaussian case) in which the role of translation operators is played by a fixed family of generalized translation operators.

Brief Communications (Ukrainian)

To the memory of Valentin Anatol'evich Zmorovich

Baranovskii F. T., Berezansky Yu. M., Buldygin V. V., Daletskii Yu. L., Dobrovol'skii V. A., Dzyadyk V. K., Lozovik V. G., Mitropolskiy Yu. A., Samoilenko A. M., Skrypnik I. V., Tamrazov P. M., Yaremchuk F. P.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 8. - pp. 1110–1111

Brief Communications (Ukrainian)

Mark Grigor'evich Krein

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 

Article (Russian)

Spectral approach to white noise analysis

Berezansky Yu. M., Livinskii V. O., Lytvynov E. V.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 177–197

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.

Anniversaries (Russian)

Samuil Davidovich Eidelman (On his sixtieth birthday)

Berezansky Yu. M., Gorbachuk M. L., Ivasyshen S. D., Korolyuk V. S., Mitropolskiy Yu. A., Skrypnik I. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1991. - 43, № 5. - pp. 578

Article (Russian)

Inverse problem of the spectral analysis and non-Abelian chains of nonlinear equations

Berezansky Yu. M., Gekhtman M. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 6. - pp. 730–747

Article (Russian)

Nonisospectral nonlinear difference equations

Berezansky Yu. M., Shmoish M. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1990. - 42, № 4. - pp. 555–558

Article (Ukrainian)

Expansion in eigenfunctions of families of commuting operators and representations of commutation relations

Berezansky Yu. M., Ostrovskii V. L., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1988. - 40, № 1. - pp. 106-109

Article (Ukrainian)

Decomposition of positive functionals on commutative *-algebras

Berezansky Yu. M., Lassner G., Yakovlev V. S.

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Ukr. Mat. Zh. - 1987. - 39, № 5. - pp. 638–641

Article (Ukrainian)

Stochastic operator integrals

Berezansky Yu. M., Us G. F., Zhernakov N. V.

Full text (.pdf)

Ukr. Mat. Zh. - 1987. - 39, № 2. - pp. 144-149

Article (Ukrainian)

Hypercomplex systems originating from orthogonal polynomials

Berezansky Yu. M., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 275–284

Article (Ukrainian)

Integration of some chains of nonlinear difference equations by the method of the inverse spectral problem

Berezansky Yu. M., Gekhtman M. I., Shmoish M. E.

Full text (.pdf)

Ukr. Mat. Zh. - 1986. - 38, № 1. - pp. 84–89

Article (Ukrainian)

A remark about the forced Toda lattice

Berezansky Yu. M.

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Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 352–355

Article (Ukrainian)

Projective spectral theorem

Berezansky Yu. M.

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Ukr. Mat. Zh. - 1985. - 37, № 2. - pp. 146 – 154

Article (Ukrainian)

Development of functional analysis at the Institute of Mathematics of the USSR Academy of Sciences

Berezansky Yu. M., Gorbachuk V. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 5. - pp. 559 – 567

Article (Ukrainian)

Representations of hypercomplex systems with locally compact basis

Berezansky Yu. M., Kalyuzhnyi A. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1984. - 36, № 4. - pp. 417 - 421

Article (Ukrainian)

Nuclear function spaces on the base of a hypercomplex system

Berezansky Yu. M., Kalyuzhnyi A. A.

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Ukr. Mat. Zh. - 1983. - 35, № 1. - pp. 9—17

Article (Ukrainian)

Self-adjointness conditions for elliptic operators with infinitely many variables

Berezansky Yu. M., Mikhailyuk T. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1977. - 29, № 2. - pp. 157–165

Article (Ukrainian)

A remark on essential self-adjointness of powers of an operator

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 6. - pp. 790–793

Article (Russian)

Self-conjugate elliptic operators with singular potential

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1974. - 26, № 5. - pp. 579–590

Article (Ukrainian)

Nuclear spaces of functions of infinitely many variables

Berezansky Yu. M., Samoilenko Yu. S.

Full text (.pdf)

Ukr. Mat. Zh. - 1973. - 25, № 6. - pp. 723—737

Article (Ukrainian)

Positive definite functions of infinitely many variables in a layer

Berezansky Yu. M., Gali I. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 4. - pp. 435–464

Article (Ukrainian)

On the scattering problem in axiomatic field theory

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1972. - 24, № 3. - pp. 399—406

Article (Ukrainian)

The generalized degree symmetric moment problem

Berezansky Yu. M., Shifrin S. N.

Full text (.pdf)

Ukr. Mat. Zh. - 1971. - 23, № 3. - pp. 291–306

Article (Ukrainian)

On the generalized power problem of moments

Berezansky Yu. M.

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Ukr. Mat. Zh. - 1970. - 22, № 4. - pp. 435–460

Article (Ukrainian)

Basic results of studies at the mathematical-analysis department of the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR

Berezansky Yu. M., Gorbachuk M. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 6. - pp. 73–92

Article (Ukrainian)

A theorem on homeomorphisms and the Green's function for general elliptic boundary problems

Berezansky Yu. M., Roitberg Ya. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 5. - pp. 3–32

Article (Ukrainian)

Integral representation of positive-definite functionals of Wightman type

Berezansky Yu. M.

Full text (.pdf)

Ukr. Mat. Zh. - 1967. - 19, № 1. - pp. 89–95

Brief Communications (Russian)

On the continuation of positively definite functions of two variables

Berezansky Yu. M., Gorbachuk M. L.

Full text (.pdf)

Ukr. Mat. Zh. - 1965. - 17, № 5. - pp. 96-102

Article (Russian)

Existence of weak solutions of certain boundary value problems for equations of mixed type

Berezansky Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 4. - pp. 347-364

The differential equation of mixed type $$Lu =\sum^2_{j, k=1}D_j (b_{jk} (x) D_ku) + \sum^2_{j=1}p_i(x)D_ju + p(x)u = f(x)$$ is considered in a bounded domain of the $(x_1, x_2)$-plane, the equation being for $x_2 > 0$ elliptic and for $x_2 < 0$ of the form $k(x_2) D^2_1u + D^2_2u = f(x)$. For boundary conditions of the Tricomi type, as well as for more general conditions, two energetic inequalities are proved (for the original and adjoint problems). The existence of the weak and the uniqueness of the strong solutions follows directly for the problems under consideration. Similar problems are investigated for certain unbounded domains.

Brief Communications (Russian)

On the smoothness up to the boundary of the nuclear region of an elliptical operator resolvent

Berezansky Yu. M., Roitberg Ya. A.

Full text (.pdf)

Ukr. Mat. Zh. - 1963. - 15, № 2. - pp. 185-189

Brief Communications (Russian)

A remark concerning the growth of eigen functions of self - adjoint operators

Berezansky Yu. M., Orochko Yu. B.

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Ukr. Mat. Zh. - 1962. - 14, № 2. - pp. 180-184

Article (Russian)

Über Randautgabe von Dirichlet Typus fur Schwingungsgleichung der Saite

Berezansky Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1960. - 12, № 4. - pp. 363 - 372

In diese Arbeit untersuchen wir in beschränkte Gebiet G mit Grenze T die Randaufgabe. Wir beweisen, daß solche Gebiete G existieren, in welche unsere Aufgabe hat schwache Lösung für beliebige / und die Lösbarkeit ist stabil über kleine Änderung der Grenze. Wir untersuchen auch die Glattheit der schwache Lösung.