2019
Том 71
№ 10

Trigub R. M.

Articles: 7
Article (Russian)

On the approximation of functions by polynomials and entire functions of exponential type

Ukr. Mat. Zh. - 2019. - 71, № 2. - pp. 293-300

We present a brief survey of works in the approximation theory of functions known to the author and connected with V. K. Dzyadyk’s scientific publications.

Article (Russian)

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.

Anniversaries (Ukrainian)

Motornyi Vitalii Pavlovych (on his 75th birthday)

Ukr. Mat. Zh. - 2015. - 67, № 7. - pp. 995-999

Anniversaries (Ukrainian)

Major Pylypovych Timan (on his 90th birthday)

Ukr. Mat. Zh. - 2013. - 65, № 8. - pp. 1141-1144

Article (Russian)

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.

Article (Russian)

On Fourier multipliers and absolute convergence of Fourier integrals of radial functions

Ukr. Mat. Zh. - 2010. - 62, № 9. - pp. 1280–1293

We obtain sufficient conditions for the representability of a function in the form of an absolutely convergent Fourier integral. These conditions are given in terms of the joint behavior of the function and its derivatives at infinity, and their efficiency and exactness are verified with the use of a known example. We also consider radial functions of an arbitrary number of variables.

Article (Ukrainian)

Multipliers of Fourier series

Ukr. Mat. Zh. - 1991. - 43, № 12. - pp. 1686–1693