2019
Том 71
№ 8

# Lopotko O. V.

Articles: 5
Brief Communications (Ukrainian)

### Integral representation of even positive-definite functions of two variables

Ukr. Mat. Zh. - 2011. - 63, № 6. - pp. 844-853

We obtain integral representation of even functions of two variables, for which the kernel $[k_1( x + y) + k_2( x - y)],\quad x, y \in R^2$, is positive definite.

Brief Communications (Ukrainian)

### Integral representation of even positive-definite functions of one variable

Ukr. Mat. Zh. - 2010. - 62, № 2. - pp. 281 – 284

We obtain an integral representation of even positive-definite functions of one variable for which the kernel $[k_1(x + y) + k_2 (x − y)]$ is positive definite.

Brief Communications (Russian)

### On the extension of even-positive-definite functions of one and two variables

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1577–1581

We prove theorems on the extension of even-positive-definite functions from a finite interval to the entire axis and from a strip onto the entire plane.

Brief Communications (Russian)

### Representations of the additive group of a nuclear space in terms of self-adjoint operators

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 271–274

We prove theorems on integral representations of the additive group of a real nuclear space in terms of self-adjoint operators. We assume that algebraic relations are realized in a dense invariant set of integral vectors.

Article (Ukrainian)

### Integral representation of evenly positive-definite bounded functions of infinite number of variables

Ukr. Mat. Zh. - 1982. - 34, № 3. - pp. 378—380