2018
Том 70
№ 8

# Gorbachuk V. I.

Articles: 33
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)

### On one generalization of the Berezanskii evolution criterion for the self-adjointness of operators

Ukr. Mat. Zh. - 2000. - 52, № 5. - pp. 608-615

We describe all weak solutions of a first-order differential equation in a Banach space on (0, ∞) and investigate their behavior in the neighborhood of zero. We use the results obtained to establish necessary and sufficient conditions for the essential maximal dissipativity of a dissipative operator in a Hilbert space.

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)

### Fourier series of periodic ultradistributions

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