Dzyadyk, Vladislav Kirillovich

Vladislav Kirillovich Dzyadyk
Vladislav Kirillovich Dzyadyk
Date of Birth	February 18, 1919
Place of Birth	Ukrainian SSR , Poltava province , pos. Sakhnovschina
Date of death	October 26, 1998 (aged 79)
Place of death	Kiev city
A country	USSR → Ukraine
Scientific field	mathematician
Place of work	, Institute of Mathematics of NASU , Kiev University
Alma mater	Dnepropetrovsk University
Academic degree
supervisor	S. M. Nikolsky , A. F. Timan
Famous students	A.I. Stepanets
Site	V.K.Dzyadyk

Vladislav Kirillovich Dzyadyk (* February 18, 1919 , Sakhnovschina , now Kharkiv Oblast - † October 26, 1998 , Kiev ) - Soviet and Ukrainian mathematician . Professor , (1969). Soros professor (1995-1998).

Scientific work

In 1951, a student at DGU solved ^[3] ^{[4] the} problem of J. Favard ^[5] . Later, he also found ^[6] an accurate estimate of ^{[7] the} best approximation $\displaystyle E_{n}(W^{s})$ ${\ displaystyle \ displaystyle E_ {n} (W ^ {s})}$ $\displaystyle E_{n}(W^{s})$ on the class of periodic functions $\displaystyle W^{s}\ (0<s<1)$ ${\ displaystyle \ displaystyle W ^ {s} \ (0 <s <1)}$ $\displaystyle W^{s}\ (0<s<1)$ :

$E_{n}(W^{s})=E_{n}(W_{1}^{(s)})_{L}={\frac {K_{s}}{n^{s}}}\sin {\frac {s\pi }{2}},\ \ \ 0<s<1,$ ${\ displaystyle E_ {n} (W ^ {s}) = E_ {n} (W_ {1} ^ {(s)}) _ {L} = {\ frac {K_ {s}} {n ^ {s }}} \ sin {\ frac {s \ pi} {2}}, \ \ \ 0 <s <1,}$ Where $K_{s}={\frac {4}{\pi }}\sum _{k=0}^{\infty }\left(2k+1\right)^{-(s+1)}={\frac {4}{\pi }}\lambda (s+1),$ ${\ displaystyle K_ {s} = {\ frac {4} {\ pi}} \ sum _ {k = 0} ^ {\ infty} \ left (2k + 1 \ right) ^ {- (s + 1)} = {\ frac {4} {\ pi}} \ lambda (s + 1),}$

Where $\displaystyle \lambda (s+1)$ ${\ displaystyle \ displaystyle \ lambda (s + 1)}$ - $\displaystyle \lambda$ ${\ displaystyle \ displaystyle \ lambda}$ -function ^[8] Dirichlet .

Constants $\displaystyle K_{s}$ ${\ displaystyle \ displaystyle K_ {s}}$ defined at $\displaystyle 0<s<1$ ${\ displaystyle \ displaystyle 0 <s <1}$ differ from Favard's constants $K_{r}={\frac {4}{\pi }}\sum _{k=0}^{\infty }\left[{\frac {(-1)^{k}}{2k+1}}\right]^{r+1}$ ${\ displaystyle K_ {r} = {\ frac {4} {\ pi}} \ sum _ {k = 0} ^ {\ infty} \ left [{\ frac {(-1) ^ {k}} {2k +1}} \ right] ^ {r + 1}}$ which are defined for integer non-negative $\displaystyle r.$ ${\ displaystyle \ displaystyle r.}$ However, note that $\displaystyle {\mathrel {\mathop {\lim \limits _{s\to 0}} }}K_{s}\sin {\frac {s\pi }{2}}=1=K_{0},\ K_{s}\sin \left.{\frac {s\pi }{2}}\right|_{s=1}=K_{1}={\frac {\pi }{2}}.$ ${\ displaystyle \ displaystyle {\ mathrel {\ mathop {\ lim \ limits _ {s \ to 0}}}} K_ {s} \ sin {\ frac {s \ pi} {2}} = 1 = K_ {0 }, \ K_ {s} \ sin \ left. {\ Frac {s \ pi} {2}} \ right | _ {s = 1} = K_ {1} = {\ frac {\ pi} {2}} .}$

In 1968-1998 he built the fundamental foundations of the approximation theory of differential and integral equations, in particular, he developed Dzyadyk methods ( a- method, AI- method), Dzyadyk transformation .

In 1963 he created a department of function theory at the Institute of Mathematics of the Academy of Sciences of the Ukrainian SSR , which he headed until 1990.

Head of the Department of Mathematical Analysis, KSU (1962-1968). Professor of KSU since 1967.

Corresponding Member of the Academy of Sciences of the Ukrainian SSR (elected December 26, 1969).

Pupils

7 doctors of sciences (until 1998), 45 candidates of sciences (of which, by 01/01/2011, 8 doctors) . There are sites:

Stepanets Alexander Ivanovich (cand. 1968, doct. 1974)
Shevchuk Igor Aleksandrovich (Cand. 1973, doct. 1985)
Podlipenko Yuri Konstantinovich (Cand. 1977, Doct. 1993)
Golub Anatoly Petrovich (cand. 1983, doct. 2010)
Bakan Andrey Gennadievich (cand. 1986, doct. 2009)
Chyp Maxim Nikolaevich (cand. 1986)

Monographs

Dzyadyk V.K. Introduction to the theory of uniform approximation of functions by polynomials. - Science, M., 1977 .-- 512 p.
Dzyadyk V.K., Approximation Methods for Solving Differential and Integral Equations / Institute of Mathematics, Academy of Sciences of the Ukrainian SSR. - Naukova Dumka, K., 1988 .-- 304 p.
Dzyadik V.K. Mathematical analysis. Volume 1 - Vishcha school, Kiev, 1995. - 495 p.
Dzyadyk VK Approximation Methods for Solutions of Differential and Integral Equations . - VSP, Utrecht-Tokyo, 1995 .-- 325 p. ISBN 90-6764-194-4
Andrievskii VV, Belyi VI, Dzjadyk VK Conformal invariants in constructive theory of functions of complex variable. Translated from the Russian by DN Kravchuk. Advanced Series in Mathematical Science and Engineering, 1. World Federation Publishers Company, Atlanta, GA, 1995. x + 199 pp. ISBN 1-885978-04-9 .
Andrievsky V.V., Belyi V.I., Dzyadyk V.K. Conformal invariants in the constructive theory of functions of a complex variable. - Naukova Dumka, Kiev, 1998 .-- 224 p. ISBN 5-12-004258-9 .
Dzyadyk Vladislav K., Shevchuk Igor A. Theory of Uniform Approximation of Functions by Polynomials . - Walter de Gruyter, 2008 .-- 480 p.

Conferences in memory of V. K. Dzyadyk

1999 - International Conference on Approximation Theory and its Applications dedicated to the memory of VK Dzyadyk . May 26-31, 1999, Kyiv
2009 - Functional Methods in Approximation Theory and Operator Theory III. Conference dedicated to the memory of V. K. Dzyadyk (1919-1998) . August 22-26, 2009. Camp Hart ^[9] , Village Svityaz , Shatskyi Region , Volyn , Ukraine. - This conference was held as part of the Ukrainian Mathematical Congress 2009

Notes

↑ Just in February 1919, Sakhnovschina was located in the territory of the newly proclaimed USSR, see the Provisional Workers 'and Peasants' Government of Ukraine
↑ V. F. Vlasov, A. N. Kolmogorov, V. G. Ponomarenko, V. N. Trofimov, D. B. Yudin, Alexander Filippovich Timan (on his sixtieth birthday) , UMN , 36 : 2 (218) ( 1981 ), 221-225
↑ V.K. Dzyadyk. On the best approximation on average of periodic functions with singularities. DAN USSR, 77 : 6 (1951), 949–952
↑ V.K. Dzyadyk. On the best approximation on the classes of periodic functions defined by kernels, which are integrals of absolutely monotone functions. IAN USSR. Ser. mat. 23 (1959), 933–950
↑ Favard problem
↑ V.K. Dzyadyk. On the best approximation on the class of periodic functions having a bounded sth derivative (0 < s <1). IAN USSR, ser. Mat., 17 (1953), 135—162
↑ S. B. Stechkin and approximation theory
↑ Dirichlet Lambda Function
↑ Garth Campus Archived May 26, 2008 on Wayback Machine

Articles about V.K.Dzyadyka

Korneychuk N.P., Nikolsky S.M., Shevchuk I.A. Vladislav Kirillovich Dzyadyk (on his sixtieth birthday) // Uspekhi Matematicheskikh Nauk. - 1979. - T. 34 , No. 4 (208) . - S. 231-237 .
Nikolsky S. M., Korneichuk N. P., Shevchuk I. A. Vladislav Kirillovich Dzyadyk (on his seventieth birthday) // Uspekhi Matematicheskikh Nauk. - 1989. - 44. - No. 4 (268). - C.243-244.
On the occasion of the 70th birthday of Corresponding Member of the Academy of Sciences of the Ukrainian SSR V.K. mat. journal - 1989. - 41 , No. 4. - C.435.
Stepanets A.I. Investigations of V.K. Dzyadyk on the theory of approximation of periodic functions // Ukrain. mat. journal - 1989 .-- 41 , N4. - S. 436-441.
Belyi V.I., Golub A.P., Shevchuk I.A. Investigations of V.K. Dzyadyk on the theory of approximation of functions of a complex variable // Ukrain. mat. journal - 1989 .-- 41 , N4. - S. 441-454.
Bilenko V.I., Konovalov V.N., Lukovsky I.A., Luchka A. Yu., Pukhov G.E., Ronto N.I. Approximation methods Dzyadyka for solving differential and integral equations // Ukrain. mat. journal - 1989 .-- 41 , N4. - S. 454-465.
Vladislav Kirillovich Dzyadyk, Corresponding Member of the NAS of Ukraine (on the occasion of his 75th birthday) // Ukr. mat. journal - 1994 .-- 46 , N4. - S. 315.
Vladislav Kirillovich Dzyadyk (1919-1998) // Ukr. mat. journal - 1998 .-- 50 , N12. - S. 1721.
Vladislav Kirillovich Dzyadyk (on the occasion of his 80th birthday) // Ukr. mat. journal - 1999 .-- 51 , N5. - S. 581-582.

Links

Corresponding Member of the National Academy of Sciences of Ukraine Dzyadik Vladislav Kirilovich .
V.K. Dzyadyk (1919-1998) // Memorial page
Dzyadyk, Vladislav Kirillovich // Dictionaries and Encyclopedias on the Academician. Big biographical encyclopedia.
Dzyadyk Vladislav Kirillovich // Publications in the Math-Net.Ru database. © Mathematical Institute. V.A. Steklova RAS , 2012

[1] Just in February 1919, Sakhnovschina was located in the territory of the newly proclaimed USSR, see the Provisional Workers 'and Peasants' Government of Ukraine

[2] V. F. Vlasov, A. N. Kolmogorov, V. G. Ponomarenko, V. N. Trofimov, D. B. Yudin, Alexander Filippovich Timan (on his sixtieth birthday) , UMN , 36 : 2 (218) ( 1981 ), 221-225

[3] V.K. Dzyadyk. On the best approximation on average of periodic functions with singularities. DAN USSR, 77 : 6 (1951), 949–952

[4] V.K. Dzyadyk. On the best approximation on the classes of periodic functions defined by kernels, which are integrals of absolutely monotone functions. IAN USSR. Ser. mat. 23 (1959), 933–950

[5] Favard problem

[6] V.K. Dzyadyk. On the best approximation on the class of periodic functions having a bounded sth derivative (0 < s <1). IAN USSR, ser. Mat., 17 (1953), 135—162

[7] S. B. Stechkin and approximation theory

[8] Dirichlet Lambda Function

[9] Garth Campus Archived May 26, 2008 on Wayback Machine

Vladislav Kirillovich Dzyadyk

Date of Birth	February 18, 1919 ( 1919-02-18 )
Place of Birth	Ukrainian SSR ^[1] , Poltava province , pos. Sakhnovschina
Date of death	October 26, 1998 ( 1998-10-26 ) (aged 79)
Place of death	Kiev city
A country	USSR → Ukraine
Scientific field	mathematician
Place of work	, Institute of Mathematics of NASU , Kiev University
Alma mater	Dnepropetrovsk University
Academic degree
supervisor	S. M. Nikolsky , A. F. Timan ^[2]
Famous students	A.I. Stepanets
Site	V.K.Dzyadyk