# Kotova O. V.

### A New Sufficient Condition for Belonging to the Algebra of Absolutely Convergent Fourier Integrals and Its Application to the Problems of Summability of Double Fourier Series

Ukr. Mat. Zh. - 2015. - 67, № 8. - pp. 1082-1096

We establish a general sufficient condition for the possibility of representation of functions $$f\left( \max \left\{\left|{x}_1\right|,\left|{x}_2\right|\right\}\right)$$ in the form of absolutely convergent double Fourier integrals and study the possibility of its application to various problems of summability of double Fourier series, in particular, by using the Marcinkiewicz–Riesz method.

### Exact order of approximation of periodic functions by one nonclassical method of summation of Fourier series

Ukr. Mat. Zh. - 2012. - 64, № 7. - pp. 954-969

By using an exact estimate for approximation by known trigonometric polynomials, we strengthen a Jackson-type theorem. Moreover, we determine the exact order of approximation of some periodic functions by these polynomials. For this purpose, we introduce a special modulus of smoothness.

### Continuum cardinality of the set of solutions of one class of equations that contain the function of frequency of ternary digits of a number

Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1414–1421

We study the equation *v*_{1 }(*x*) = *x*, where *v*_{1 }(*x*) is the function of frequency of the digit 1 in ternary expansion of *x*.
We prove that this equation has a unique rational solution and a continuum set of irrational solutions.
An algorithm for the construction of solutions is proposed. We also describe the topological and metric properties of the set of all solutions.
Some additional facts about equations *v _{i }*(

*x*),

*i*= 0,2, are also given.