2019
Том 71
№ 11

Berezansky Yu. M.

Articles: 62
Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 80th birthday)

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)

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

Anniversaries (Ukrainian)

Yurii Stephanovych Samoilenko (on his 70th birthday)

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

Anniversaries (Ukrainian)

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

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

Anniversaries (Ukrainian)

Anatolii Mykhailovych Samoilenko (on his 75th birthday)

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

Anniversaries (Ukrainian)

Yuri Yurievich Trokhimchuk (on his 80th birthday)

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

Article (Ukrainian)

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

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

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)

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

Anniversaries (Ukrainian)

Leonіd Andrіyovich Pastur (on his 70th birthday)

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

Article (English)

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

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)

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

Article (English)

A generalization of an extended stochastic integral

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)

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

Anniversaries (Ukrainian)

On the 90th birthday of Yurii Alekseevich Mitropol’skii

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

Anniversaries (Ukrainian)

Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

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

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

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

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

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)

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

Anniversaries (Ukrainian)

Igor Volodymyrovych Skrypnik (On His 60th Birthday)

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

Article (English)

On the Theory of Generalized Toeplitz Kernels

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

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)

Anatolii Mikhailovich Samoilenko (on his 60th birthday)

Ukr. Mat. Zh. - 1998. - 50, № 1. - pp. 3–4

Anniversaries (Ukrainian)

Yurii L’vovich Daletskii

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

Article (Ukrainian)

Infinite-dimensional analysis related to generalized translation operators

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.

Anniversaries (Ukrainian)

Aleksandr Nikolaevich Sharkovsky (on his 60th birthday)

Ukr. Mat. Zh. - 1996. - 48, № 12. - pp. 1602-1603

Anniversaries (Ukrainian)

On the 60th birthday of Leonid Pavlovich Nizhnik

Ukr. Mat. Zh. - 1995. - 47, № 10. - pp. 1416–1417

Article (Russian)

On a nonlocal problem for a parabolic equation

Ukr. Mat. Zh. - 1995. - 47, № 6. - pp. 790–800

We study a nonlocal boundary-value problem for a parabolic equation in a two-dimensional domain, establish ana priori estimate in the energy norm, prove the existence and uniqueness of a generalized solution from the classW 2 1,0 (Q T ), and construct a difference scheme for the second-order approximation.

Brief Communications (Ukrainian)

To the memory of Valentin Anatol'evich Zmorovich

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

Anniversaries (Ukrainian)

Mark Grigor'evich Krein

Ukr. Mat. Zh. - 1994. - 46, № 3. - pp. 146

Article (Russian)

Spectral approach to white noise analysis

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)

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

Article (Russian)

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

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

Article (Russian)

Nonisospectral nonlinear difference equations

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

Article (Ukrainian)

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

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

Article (Ukrainian)

Decomposition of positive functionals on commutative *-algebras

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

Article (Ukrainian)

Stochastic operator integrals

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

Article (Ukrainian)

Hypercomplex systems originating from orthogonal polynomials

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

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

Article (Ukrainian)

A remark about the forced Toda lattice

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

Article (Ukrainian)

Projective spectral theorem

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

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

Article (Ukrainian)

Representations of hypercomplex systems with locally compact basis

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

Article (Ukrainian)

Nuclear function spaces on the base of a hypercomplex system

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

Article (Ukrainian)

Self-adjointness conditions for elliptic operators with infinitely many variables

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

Article (Ukrainian)

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

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

Article (Russian)

Self-conjugate elliptic operators with singular potential

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

Article (Ukrainian)

Nuclear spaces of functions of infinitely many variables

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

Article (Ukrainian)

Positive definite functions of infinitely many variables in a layer

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

Article (Ukrainian)

On the scattering problem in axiomatic field theory

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

Article (Ukrainian)

The generalized degree symmetric moment problem

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

Article (Ukrainian)

On the generalized power problem of moments

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

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

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

Article (Ukrainian)

Integral representation of positive-definite functionals of Wightman type

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

Brief Communications (Russian)

On the continuation of positively definite functions of two variables

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

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

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

Brief Communications (Russian)

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

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

Article (Russian)

Über Randautgabe von Dirichlet Typus fur Schwingungsgleichung der Saite

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.