# zbMATH — the first resource for mathematics

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 Documents Indexed: 44 Publications since 1977
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#### Co-Authors

 17 single-authored 8 Dolzhenko, Evgeniĭ Prokof’evich 3 Chunaev, Petr 3 Danchenko, D. Ya. 3 Kondakova, E. N. 2 Chunaev, P. V. 2 Dodonov, A. E. 2 Vasilchenkova, D. G. 1 Chkalova, D. G. 1 Davydov, Alekseĭ Aleksandrovich 1 Komarov, Mikhaĭl Anatol’evich 1 Rubay, Roman Vasil’evich 1 Semin, Lev A. 1 Zvyagin, M. Yu
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#### Serials

 9 Journal of Mathematical Sciences (New York) 5 Sbornik: Mathematics 5 Proceedings of the Steklov Institute of Mathematics 4 Mathematical Notes 3 Mathematics of the USSR. Izvestiya 3 Russian Mathematics 2 Journal of Approximation Theory 2 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 1 Analysis Mathematica 1 Moscow University Mathematics Bulletin 1 Siberian Mathematical Journal 1 Soviet Mathematics. Doklady 1 Mathematics of the USSR, Sbornik 1 Russian Academy of Sciences. Sbornik. Mathematics 1 Russian Academy of Sciences. Doklady. Mathematics 1 St. Petersburg Mathematical Journal 1 Izvestiya: Mathematics 1 Complex Analysis and Operator Theory
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#### Fields

 32 Functions of a complex variable (30-XX) 15 Approximations and expansions (41-XX) 5 Potential theory (31-XX) 4 Real functions (26-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 2 Integral equations (45-XX) 2 Numerical analysis (65-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Biology and other natural sciences (92-XX)

#### Citations contained in zbMATH Open

34 Publications have been cited 181 times in 83 Documents Cited by Year
Approximation by simple fractions. Zbl 1025.30001
Danchenko, V. I.; Danchenko, D. Ya.
2001
Chebyshev’s alternance in the approximation of constants by simple partial fractions. Zbl 1214.41004
Danchenko, V. I.; Kondakova, E. N.
2010
Estimates of derivatives of simplest fractions and other questions. Zbl 1134.41008
Danchenko, V. I.
2006
Approximation by amplitude and frequency operators. Zbl 1346.30019
2016
Approximation by simple partial fractions and their generalizations. Zbl 1290.41008
Danchenko, V. I.; Chunaev, P. V.
2011
Convergence of simple partial fractions in $$L_p(\mathbb R)$$. Zbl 1202.41012
Danchenko, V. I.
2010
Extremal and approximative properties of simple partial fractions. Zbl 1459.41015
Danchenko, V. I.; Komarov, M. A.; Chunaev, P. V.
2018
Approximation properties of sums of the form $$\Sigma _k \lambda _k h (\lambda _k z)$$. Zbl 1160.30022
Danchenko, V. I.
2008
Existence and uniqueness of a stationary distribution of a biological community. Zbl 1231.92055
Davydov, A. A.; Danchenko, V. I.; Zvyagin, M. Yu.
2009
Estimates of the distances from the poles of logarithmic derivatives of polynomials to lines and circles. Zbl 0864.30003
Danchenko, V. I.
1994
On rational components of meromorphic functions and their derivatives. Zbl 0738.30027
Danchenko, V. I.
1990
Mapping of sets of finite $$\alpha$$-measure by means of rational functions. Zbl 0673.30004
Dolzhenko, E. P.; Danchenko, V. I.
1987
Extraction of pairs of harmonics from trigonometric polynomials by phase-amplitude operators. Zbl 1398.42001
Danchenko, V. I.; Danchenko, D. Ya.
2018
Estimates for exponential sums. Applications. Zbl 1268.30036
Danchenko, V. I.; Dodonov, A. E.
2013
Estimates for $$L_p$$-norms of simple partial fractions. Zbl 1342.30023
Danchenko, V. I.; Dodonov, A. E.
2014
Criterion for the appearance of singular nodes under interpolation by simple partial fractions. Zbl 1298.41003
Danchenko, V. I.; Kondakova, E. N.
2012
On boundary behavior of solutions of the generalized Cauchy-Riemann equations. Zbl 1029.30030
Dolzhenko, E. P.; Danchenko, V. I.
1998
Estimates of Green potentials. Applications. Zbl 1054.31001
Danchenko, V. I.
2003
On separation of singularities of meromorphic functions. Zbl 0611.30032
Danchenko, V. I.
1986
On the boundary properties of solutions to the generalized Cauchy-Riemann equation. Zbl 1079.30056
Dolzhenko, E. P.; Danchenko, V. I.
2002
Sharp quadrature formulas and inequalities between various metrics for rational functions. Zbl 1344.30028
Danchenko, V. I.; Semin, Lev A.
2016
Lengths of lemniscates. Variations of rational functions. Zbl 1139.30002
Danchenko, V. I.
2007
Several integral estimates of the derivatives of rational functions on sets of finite density. Zbl 0866.30002
Danchenko, V. I.
1996
On existence sets for Markov-Bernshtein estimates for rational functions. Zbl 1309.41005
Danchenko, V. I.; Danchenko, D. Ya.
2014
Cauchy and Poisson formulas for polyanalytic functions and applications. Zbl 1336.30066
Danchenko, V. I.
2016
Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions. Zbl 1387.41015
2018
Existence criterion for estimates of derivatives of rational functions. Zbl 1107.30007
Danchenko, V. I.
2005
On mean integral values of solutions of the generalized Cauchy-Riemann equations. Zbl 1151.30039
Danchenko, V. I.; Dolzhenko, E. P.
2007
Integral estimates of lengths of level lines of rational functions and Zolotarev’s problem. Zbl 1282.30023
Danchenko, V. I.
2013
Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions. Zbl 0392.41007
Dolzhenko, E. P.; Danchenko, V. I.
1977
An integral estimate for the derivative of a rational function. Zbl 0443.30050
Danchenko, V. I.
1980
On boundary behavior of holomorphic components of bianalytic functions. Zbl 1088.30023
Danchenko, V. I.; Dolzhenko, E. P.
2005
Extraction of several harmonics from trigonometric polynomials. Fejer-type inequalities. Zbl 1442.42006
Vasilchenkova, D. G.; Danchenko, V. I.
2020
Extraction of harmonics from trigonometric polynomials by phase-amplitude operators. Zbl 1461.42001
Vasilchenkova, D. G.; Danchenko, V. I.
2021
Extraction of harmonics from trigonometric polynomials by phase-amplitude operators. Zbl 1461.42001
Vasilchenkova, D. G.; Danchenko, V. I.
2021
Extraction of several harmonics from trigonometric polynomials. Fejer-type inequalities. Zbl 1442.42006
Vasilchenkova, D. G.; Danchenko, V. I.
2020
Extremal and approximative properties of simple partial fractions. Zbl 1459.41015
Danchenko, V. I.; Komarov, M. A.; Chunaev, P. V.
2018
Extraction of pairs of harmonics from trigonometric polynomials by phase-amplitude operators. Zbl 1398.42001
Danchenko, V. I.; Danchenko, D. Ya.
2018
Quadrature formulas with variable nodes and Jackson-Nikolskii inequalities for rational functions. Zbl 1387.41015
2018
Approximation by amplitude and frequency operators. Zbl 1346.30019
2016
Sharp quadrature formulas and inequalities between various metrics for rational functions. Zbl 1344.30028
Danchenko, V. I.; Semin, Lev A.
2016
Cauchy and Poisson formulas for polyanalytic functions and applications. Zbl 1336.30066
Danchenko, V. I.
2016
Estimates for $$L_p$$-norms of simple partial fractions. Zbl 1342.30023
Danchenko, V. I.; Dodonov, A. E.
2014
On existence sets for Markov-Bernshtein estimates for rational functions. Zbl 1309.41005
Danchenko, V. I.; Danchenko, D. Ya.
2014
Estimates for exponential sums. Applications. Zbl 1268.30036
Danchenko, V. I.; Dodonov, A. E.
2013
Integral estimates of lengths of level lines of rational functions and Zolotarev’s problem. Zbl 1282.30023
Danchenko, V. I.
2013
Criterion for the appearance of singular nodes under interpolation by simple partial fractions. Zbl 1298.41003
Danchenko, V. I.; Kondakova, E. N.
2012
Approximation by simple partial fractions and their generalizations. Zbl 1290.41008
Danchenko, V. I.; Chunaev, P. V.
2011
Chebyshev’s alternance in the approximation of constants by simple partial fractions. Zbl 1214.41004
Danchenko, V. I.; Kondakova, E. N.
2010
Convergence of simple partial fractions in $$L_p(\mathbb R)$$. Zbl 1202.41012
Danchenko, V. I.
2010
Existence and uniqueness of a stationary distribution of a biological community. Zbl 1231.92055
Davydov, A. A.; Danchenko, V. I.; Zvyagin, M. Yu.
2009
Approximation properties of sums of the form $$\Sigma _k \lambda _k h (\lambda _k z)$$. Zbl 1160.30022
Danchenko, V. I.
2008
Lengths of lemniscates. Variations of rational functions. Zbl 1139.30002
Danchenko, V. I.
2007
On mean integral values of solutions of the generalized Cauchy-Riemann equations. Zbl 1151.30039
Danchenko, V. I.; Dolzhenko, E. P.
2007
Estimates of derivatives of simplest fractions and other questions. Zbl 1134.41008
Danchenko, V. I.
2006
Existence criterion for estimates of derivatives of rational functions. Zbl 1107.30007
Danchenko, V. I.
2005
On boundary behavior of holomorphic components of bianalytic functions. Zbl 1088.30023
Danchenko, V. I.; Dolzhenko, E. P.
2005
Estimates of Green potentials. Applications. Zbl 1054.31001
Danchenko, V. I.
2003
On the boundary properties of solutions to the generalized Cauchy-Riemann equation. Zbl 1079.30056
Dolzhenko, E. P.; Danchenko, V. I.
2002
Approximation by simple fractions. Zbl 1025.30001
Danchenko, V. I.; Danchenko, D. Ya.
2001
On boundary behavior of solutions of the generalized Cauchy-Riemann equations. Zbl 1029.30030
Dolzhenko, E. P.; Danchenko, V. I.
1998
Several integral estimates of the derivatives of rational functions on sets of finite density. Zbl 0866.30002
Danchenko, V. I.
1996
Estimates of the distances from the poles of logarithmic derivatives of polynomials to lines and circles. Zbl 0864.30003
Danchenko, V. I.
1994
On rational components of meromorphic functions and their derivatives. Zbl 0738.30027
Danchenko, V. I.
1990
Mapping of sets of finite $$\alpha$$-measure by means of rational functions. Zbl 0673.30004
Dolzhenko, E. P.; Danchenko, V. I.
1987
On separation of singularities of meromorphic functions. Zbl 0611.30032
Danchenko, V. I.
1986
An integral estimate for the derivative of a rational function. Zbl 0443.30050
Danchenko, V. I.
1980
Dependence of the differentiability of functions of several variables on their rate of approximation by rational functions. Zbl 0392.41007
Dolzhenko, E. P.; Danchenko, V. I.
1977
all top 5

#### Cited by 52 Authors

 22 Danchenko, Vladimir Il’ich 19 Komarov, Mikhaĭl Anatol’evich 5 Chunaev, Petr 4 Borodin, Petr A. 4 Chunaev, P. V. 4 Danchenko, D. Ya. 3 Kondakova, E. N. 3 Pekarskij, A. A. 2 Dadashova, Irada B. 2 Dodonov, A. E. 2 Dolzhenko, Evgeniĭ Prokof’evich 2 Mamedkhanov, Jamal Islam oglu 2 Nikolaev, Mikhaĭl V. 2 Sachkov, Yuriĭ Leonidovich 2 Vasilchenkova, D. G. 1 Abakumov, Evgeny V. 1 Akturk, Mehmet Ali 1 Baranov, Anton D. 1 Bespalov, Mikhaĭl Sergeevich 1 Bodrov, A. G. 1 Borichev, Aleksandr Aleksandrovich 1 Chkalova, D. G. 1 Cui, Yanyan 1 Dyuzhina, N. A. 1 Fedorovskiy, Konstantin Yu. 1 Fryantsev, A. V. 1 Galkin, E. G. 1 Gauthier, Paul M. 1 Huhtanen, Marko 1 Kalistratova, A. V. 1 Kayumov, Fanil’ Damirovich 1 Kayumova, A. V. 1 Khatamov, Akhtam 1 Kosukhin, Oleg N. 1 Larina, Yana Yur’evna 1 Li, Zunfeng 1 Lukashov, Alexey L. 1 Mardvilko, Tat’yana Sergeevna 1 Nevanlinna, Olavi 1 Nigmatyanova, Yu. M. 1 Nikol’skiĭ, Nikolaĭ Kapitonovich 1 Novak, Ya. V. 1 Qiao, Yuying 1 Ramazanov, A. K. 1 Rodina, Lyudmila Ivanova 1 Rubay, Roman Vasil’evich 1 Savost’yanov, A. S. 1 Semin, Lev A. 1 Shklyaev, Konstantin S. 1 Vakarchuk, Mihail B. 1 Wang, Liping 1 Zarouf, Rachid
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#### Cited in 25 Serials

 23 Journal of Mathematical Sciences (New York) 16 Mathematical Notes 7 Russian Mathematics 4 Journal of Approximation Theory 4 St. Petersburg Mathematical Journal 4 Proceedings of the Steklov Institute of Mathematics 3 Moscow University Computational Mathematics and Cybernetics 2 Siberian Mathematical Journal 2 Izvestiya: Mathematics 2 Doklady Mathematics 2 Complex Variables and Elliptic Equations 1 Journal of Mathematical Analysis and Applications 1 Mathematische Annalen 1 Numerische Mathematik 1 Indagationes Mathematicae. New Series 1 Bulletin des Sciences Mathématiques 1 Sbornik: Mathematics 1 Abstract and Applied Analysis 1 Journal of Dynamical and Control Systems 1 Lobachevskii Journal of Mathematics 1 Differential Equations 1 Complex Analysis and Operator Theory 1 Journal of Classical Analysis 1 Problemy Analiza. Issues of Analysis 1 Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
all top 5

#### Cited in 20 Fields

 42 Functions of a complex variable (30-XX) 41 Approximations and expansions (41-XX) 7 Numerical analysis (65-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Biology and other natural sciences (92-XX) 5 Real functions (26-XX) 4 Integral equations (45-XX) 3 Operator theory (47-XX) 3 Systems theory; control (93-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 General and overarching topics; collections (00-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Information and communication theory, circuits (94-XX)