2018
Том 70
№ 4

Gorbachuk V. I.

Articles: 32
Anniversaries (Ukrainian)

Mark Grigorievich Krein (to the centenary of his birth)

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

Article (Ukrainian)

On the behavior of orbits of uniformly stable semigroups at infinity

Ukr. Mat. Zh. - 2006. - 58, № 2. - pp. 148–159

For uniformly stable bounded analytic $C_0$-semigroups $\{T(t)\} t ≥ 0$ of linear operators in a Banach space $B$, we study the behavior of their orbits $T (t)x, x ∈ B$, at infinity. We also analyze the relationship between the order of approaching the orbit $T (t)x$ to zero as $t → ∞$ and the degree of smoothness of the vector $x$ with respect to the operator $A^{-1}$ inverse to the generator A of the semigroup $\{T(t)\}_{t \geq 0}$. In particular, it is shown that, for this semigroup, there exist orbits approaching zero at infinity not slower than $e^{-at^{\alpha}}$, where $a > 0,\; 0 < \alpha < \pi/(2 (\pi - 0 )),\; \theta$ is the angle of analyticity of $\{T(t)\}_{t \geq 0}$, and the collection of these orbits is dense in the set of all orbits.

Anniversaries (Ukrainian)

Leonid Pavlovych Nyzhnyk (on his 70-th birthday)

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

Anniversaries (Ukrainian)

Yurij Makarovich Berezansky (the 80th anniversary of his birth)

Ukr. Mat. Zh. - 2005. - 57, № 5. - pp. 3-11

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)

Behavior of the extended spectral measure of a self-adjoint operator at infinity

Ukr. Mat. Zh. - 1997. - 49, № 4. - pp. 510–516

We study the dependence of the rate of growth of the extended spectral measure of a self-adjoint operator at infinity on the order of singularity of the vector on which this measure is considered.

Article (Ukrainian)

Theory of self-adjoint extensions of symmetric operators. entire operators and boundary-value problems

Ukr. Mat. Zh. - 1994. - 46, № 1-2. - pp. 55–62

Article (Ukrainian)

Extension theory for symmetric operators and boundary value problems for differential equations

Ukr. Mat. Zh. - 1989. - 41, № 10. - pp. 1299–1313

Article (Ukrainian)

Inverse theorems of approximation by biharmonic functions

Ukr. Mat. Zh. - 1986. - 38, № 5. - pp. 569–575

Article (Ukrainian)

Inverse theorems for approximation by harmonic functions

Ukr. Mat. Zh. - 1986. - 38, № 3. - pp. 309–314

Article (Ukrainian)

Yurii Makarovich Berezansky (on his sixtieth birthday)

Ukr. Mat. Zh. - 1985. - 37, № 3. - pp. 342–343

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)

A study of certain boundary properties of solutions of the equation Δu - c ² u = 0 in the half plane

Ukr. Mat. Zh. - 1983. - 35, № 6. - pp. 681-688

Article (Ukrainian)

The Fatou theorem on the boundary behavior of derivatives in the class of biharmonic functions

Ukr. Mat. Zh. - 1983. - 35, № 5. - pp. 557—562

Article (Ukrainian)

Spaces of infinitely differentiable vectors of a nonnegative self-adjoint operator

Ukr. Mat. Zh. - 1983. - 35, № 5. - pp. 617—621

Article (Ukrainian)

Ukr. Mat. Zh. - 1982. - 34, № 2. - pp. 144-150

Article (Ukrainian)

Estimates of the accuracy of an approximate solution of the cauchy problem for Laplace's equation in an infinite strip

Ukr. Mat. Zh. - 1980. - 32, № 6. - pp. 731–736

Article (Ukrainian)

Conditions for the oscillation of solutions of a class of elliptic equations of high orders with constant coefficients

Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 593–600

Article (Ukrainian)

Operator calculus for some classes of non-self-adjoint operators

Ukr. Mat. Zh. - 1979. - 31, № 2. - pp. 123–131

Article (Ukrainian)

Scattering problem for first-order differential equations with operator coefficients

Ukr. Mat. Zh. - 1978. - 30, № 4. - pp. 452–461

Article (Ukrainian)

Some questions of the spectral theory of differential equations of elliptic type in the space of vector-functions

Ukr. Mat. Zh. - 1976. - 28, № 3. - pp. 313–324

Article (Ukrainian)

Some questions of the spectral theory of differential equations of elliptic type in the space of vector functions on a finite interval

Ukr. Mat. Zh. - 1976. - 28, № 1. - pp. 12–26

Article (Ukrainian)

Some properties of the Cauchy — Poisson singular integral

Ukr. Mat. Zh. - 1976. - 28, № 1. - pp. 79–82

Article (Ukrainian)

On some properties of the Hadamard products of functions which are regular in the disk

Ukr. Mat. Zh. - 1975. - 27, № 1. - pp. 74–81

Article (Ukrainian)

The spectrum of self-adjoint extensions of the minimal operator generated by a Sturm-Liouville equation with operator potential

Ukr. Mat. Zh. - 1972. - 24, № 6. - pp. 726—734

Article (Ukrainian)

Classes of boundary-value problems for the sturm — Liouville equation with an operator potential

Ukr. Mat. Zh. - 1972. - 24, № 3. - pp. 291—304

Article (Ukrainian)

The inverse problem of approximating functions on a boundary for compacta of positive capacity

Ukr. Mat. Zh. - 1972. - 24, № 2. - pp. 147—161

Article (Ukrainian)

On the pithiness of bounds in converse theorems on the approximation of functions on regular compacta of the complex plane

Ukr. Mat. Zh. - 1972. - 24, № 1. - pp. 83–92

Article (Ukrainian)

Problems of the spectral theory of the second order linear differential equation with unbounded operator coefficients

Ukr. Mat. Zh. - 1971. - 23, № 1. - pp. 3–14

Article (Ukrainian)

Continuations of a real hermite-indefinite function with a negative square

Ukr. Mat. Zh. - 1967. - 19, № 4. - pp. 119–125

Article (Russian)

On the integral representation of Hermitian-indefinite nuclei

Ukr. Mat. Zh. - 1965. - 17, № 3. - pp. 43-58

Brief Communications (Russian)

On integral representations of Hermito-indefinite nuclei (case of many variables)

Ukr. Mat. Zh. - 1964. - 16, № 2. - pp. 232-237