Zobrazeno 1 - 10
of 22
pro vyhledávání: '"V. I. Danchenko"'
Autor:
V. I. Danchenko, D. G. Chkalova
Publikováno v:
Проблемы анализа, Vol 10 (28), Iss 3, Pp 31-40 (2021)
Using the method of amplitude and phase transformations, we obtain sharp inequalities for the derivatives of real-valued trigonometric polynomials. The inequalities are sharp, as there are the corresponding extremal polynomials, for which they become
Externí odkaz:
https://doaj.org/article/b75c173fbc0944538c72c3e6895612fb
Autor:
D. G. Chkalova, V. I. Danchenko
Publikováno v:
Issues of Analysis. 28:31-40
Autor:
D. G. Vasilchenkova, V. I. Danchenko
Publikováno v:
St. Petersburg Mathematical Journal. 32:215-232
Autor:
V. I. Danchenko, D. G. Vasilchenkova
Publikováno v:
Proceedings of the Steklov Institute of Mathematics. 308:92-106
Given a trigonometric polynomial $${T_n}(t) = \sum\nolimits_{k = 1}^n {{\tau _k}\left( t \right),{\tau _k}\left( t \right): = {a_k}\cos kt + {b_k}\sin kt}$$ we consider the problem of extracting the sum of harmonics $$\sum \tau_{\mu_s}(t)$$ prescribe
Autor:
V. I. Danchenko, E. N. Kondakova
Publikováno v:
Journal of Mathematical Sciences. 239:299-308
It is known that for the best uniform approximation of real constants c by simple partial fractions ρn of order n on a real segment it is necessary and sufficient to have an alternance of n + 1 points on this segment for the difference ρn − c, n
Autor:
L. A. Semin, V. I. Danchenko
Publikováno v:
Siberian Mathematical Journal. 57:218-229
We obtain the sharp quadrature formulas for integrals of complex rational functions over circles, segments of the real axis, and the real axis itself. Among them there are formulas for calculating the L 2-norms of rational functions. Using the quadra
Autor:
V. I. Danchenko
Publikováno v:
Russian Mathematics. 60:11-21
We obtain new Cauchy and Poisson integral formulas for polyanalytic functions. As an application, we establish mean value theorems for polyanalytic and real polyharmonic functions in a disk. We also give applications to sharp estimates of generalized
Autor:
V. I. Danchenko, A. E. Dodonov
Publikováno v:
Russian Mathematics. 58:6-15
We obtain estimates for L p -norms of simple partial fractions in terms of their L r -norms on bounded and unbounded segments of the real axis for various p > 1 and r > 1 (S. M. Nikolskii type inequalities). We adduce examples and remarks concerning
Autor:
V. I. Danchenko
Publikováno v:
Mathematical Notes. 94:314-319
Integral estimates of lengths of level lines (lemniscates) of rational functions of a complex variable are obtained. These estimates are related to the problem of separation of compact sets by rational functions and to Zolotarev’s problem.
Autor:
A. E. Dodonov, V. I. Danchenko
Publikováno v:
Journal of Mathematical Sciences. 188:197-206
We obtain estimates of exponential (in particular, trigonometric) sums in terms of rational functions. Examples of sharp inequalities are given. These inequalities are used for estimating solutions to linear homogeneous differential equations with co