2019
Том 71
№ 11

# Volchkov V. V.

Articles: 6
Article (Russian)

### One Problem Connected with the Helgason Support Problem

Ukr. Mat. Zh. - 2015. - 67, № 9. - pp. 1189-1200

We solve the problem of description of the set of continuous functions in annular subdomains of the n-dimensional sphere with zero integrals over all (n - 1)-dimensional spheres covering the inner spherical cap. As an application, we establish a spherical analog of the Helgason support theorem and new uniqueness theorems for functions with zero spherical means.

Article (Russian)

### New Integral Representations for a Hypergeometric Function

Ukr. Mat. Zh. - 2001. - 53, № 4. - pp. 435-440

We obtain new integral representations for a hypergeometric function.

Article (Russian)

### Uniqueness theorems for multiple lacunary trigonometric series

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1477–1481

In a many-dimensional space, we study some properties of functions with lacunary Fourier series depending only on the values of these functions in a neighborhood of a certain point.

Article (Russian)

### Spherical means on Euclidean spaces

Ukr. Mat. Zh. - 1998. - 50, № 10. - pp. 1310–1315

We give a description of certain classes of functions with zero spherical means.

Brief Communications (Russian)

### On an equality equivalent to the Riemann hypothesis

Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 422–423

We prove that the Riemann hypothesis on zeros of the zeta function ζ(s) is equivalent to the equality $$\int\limits_0^\infty {\frac{{1 - 12t^2 }}{{(1 + 4t^2 )^3 }}dt} \int\limits_{1/2}^\infty {\ln |\varsigma (\sigma + it)|d\sigma = \pi \frac{{3 - \gamma }}{{32}},}$$ where $$\gamma = \mathop {\lim }\limits_{N \to \infty } \left( {\sum\limits_{n = 1}^N {\frac{1}{n} - \ln N} } \right)$$ is the Euler constant.

Brief Communications (Russian)

### On exact constants in Jackson-type inequalities in the space $L^2$

Ukr. Mat. Zh. - 1995. - 47, № 1. - pp. 108-110

The exact dependence of constants in Jackson-type inequalities on the rate of convergence of the Diophantine approximations of certain numbers is obtained.