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Zastavnyi, Viktor Petrovich
Statistics Math-Net.Ru
Total publications: 20
Scientific articles: 20

Number of views:
This page:4013
Abstract pages:8371
Full texts:2584
References:997
Associate professor
Doctor of physico-mathematical sciences (2013)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 25.07.1959
E-mail:
Keywords: the theory of approximation, analysis of the Fourier, positive definite and completely monotonic functions, zero of entire functions, integral transforms.
UDC: 517, 517.51, 517.518, 519.213.2, 517.5, 517.518.83, 517.521
MSC: 26a48, 26a51, 42a10, 42a15, 42a82, 42b08, 42b10, 46b04, 60e05

Subject:

Positive definite functions. Theory of Approximation and Harmonic Analysis.

Biography

Graduated from Faculty of Mathematics of Donetsk State University (DonGU) in 1981 (department of mathematical analysis and theory of functions). Ph.D. thesis was defended in 1987. A list of my works contains more than 40 titles. Since 1978 I am by the participant of a scientific seminar in DonGU the Analysis of the Fourier and theory of approximations of functions, which is supervised by R. M. Trigub.
   
Main publications:
  1. Zastavnyi V. P., “O mnozhestve nulei preobrazovaniya Fure mery i summirovaniii dvoinykh ryadov Fure metodami tipa Bernshteina–Rogozinskogo”, Ukr. matem. zhurn., 36:5 (1984), 615–621  mathscinet  zmath
  2. Zastavnyi V. P., “Polozhitelno opredelennye funktsii, zavisyaschie ot normy”, Doklady Rossiiskoi akademii nauk, 325:5 (1992), 901–903  mathscinet  zmath
  3. Zastavnyi V. P., “Positive definite functions depending on the norm”, Russian Journal of Mathematical Physics, 1993, no. 4, 511–522  mathscinet  zmath
  4. Zastavnyi V. P., “O polozhitelnoi opredelennosti nekotorykh funktsii”, Doklady RAN, 365:2 (1999), 159–161  mathscinet  zmath; angliiskii perevod: “On positive definiteness of some functions”, Dokl. Math., 59 (1999), 156–161
  5. Zastavnyi V. P., “On positive definiteness of some functions”, Journal of Multivariate Analysis, 73 (2000), 55–81  crossref  mathscinet  zmath

https://www.mathnet.ru/eng/person12481
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/213444
https://elibrary.ru/author_items.asp?spin=4324-9397
https://orcid.org/0000-0002-4833-3897
https://www.scopus.com/authid/detail.url?authorId=6508291638
https://arxiv.org/a/zastavnyi_v_1

Publications in Math-Net.Ru Citations
2024
1. V. P. Zastavnyi, “On extremal functions in inequalities for entire functions”, Mat. Zametki, 116:1 (2024),  67–76  mathnet; Math. Notes, 116:1 (2024), 58–65
2023
2. V. P. Zastavnyi, “Analog of Schoenberg's Theorem for $a$-Conditionally Negative Definite Matrix-Valued Kernels”, Mat. Zametki, 114:1 (2023),  81–93  mathnet  mathscinet; Math. Notes, 114:1 (2023), 66–76  scopus
3. V. P. Zastavnyi, “On extremal trigonometric polynomials”, Trudy Inst. Mat. i Mekh. UrO RAN, 29:4 (2023),  70–91  mathnet  elib 1
2020
4. V. P. Zastavnyi, “Inequalities for Positive Definite Functions”, Mat. Zametki, 108:6 (2020),  823–836  mathnet  mathscinet  elib; Math. Notes, 108:6 (2020), 791–801  isi  scopus 1
5. V. P. Zastavnyi, “A Generalization of Schep's Theorem on the Positive Definiteness of a Piecewise Linear Function”, Mat. Zametki, 107:6 (2020),  873–887  mathnet  mathscinet  elib; Math. Notes, 107:6 (2020), 959–971  isi  scopus 3
2019
6. V. P. Zastavnyi, “Some Problems Related to Completely Monotone Positive Definite Functions”, Mat. Zametki, 106:2 (2019),  222–240  mathnet  mathscinet  elib; Math. Notes, 106:2 (2019), 212–228  isi  scopus 1
2018
7. V. P. Zastavnyi, A. Manov, “Positive Definiteness of Complex Piecewise Linear Functions and Some of Its Applications”, Mat. Zametki, 103:4 (2018),  519–535  mathnet  mathscinet  elib; Math. Notes, 103:4 (2018), 550–564  isi  scopus 3
2017
8. V. P. Zastavnyi, A. D. Manov, “On the Positive Definiteness of Some Functions Related to the Schoenberg Problem”, Mat. Zametki, 102:3 (2017),  355–368  mathnet  mathscinet  elib; Math. Notes, 102:3 (2017), 325–337  isi  scopus 4
9. V. P. Zastavnyi, “Positive Definiteness of a Family of Functions”, Mat. Zametki, 101:2 (2017),  215–225  mathnet  mathscinet  elib; Math. Notes, 101:2 (2017), 250–259  isi  scopus 1
10. V. P. Zastavnyi, A. S. Levadnaya, “Power wight integrability for sums of moduli of blocks from trigonometric series”, Trudy Inst. Mat. i Mekh. UrO RAN, 23:3 (2017),  125–133  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 303, suppl. 1 (2018), S223–S230  isi
11. Viktor P. Zastavnyi, “Positive definite functions and sharp inequalities for periodic functions”, Ural Math. J., 3:2 (2017),  82–99  mathnet  mathscinet  elib 3
2013
12. V. P. Zastavnyi, “Asymptotics of Series Arising from the Approximation of Periodic Functions by Riesz and Cesàro Means”, Mat. Zametki, 93:1 (2013),  45–55  mathnet  mathscinet  zmath  elib; Math. Notes, 93:1 (2013), 58–68  isi  scopus
2011
13. V. P. Zastavnyi, V. V. Savchuk, “Approximation of Classes of Convolutions by Linear Operators of Special Form”, Mat. Zametki, 90:3 (2011),  351–361  mathnet  mathscinet; Math. Notes, 90:3 (2011), 333–343  isi  scopus 4
14. N. I. Goloschapova, V. P. Zastavnyi, M. M. Malamud, “Positive Definite Functions and Spectral Properties of the Schrödinger Operator with Point Interactions”, Mat. Zametki, 90:1 (2011),  151–156  mathnet  mathscinet; Math. Notes, 90:1 (2011), 149–154  isi  scopus 14
2010
15. V. P. Zastavnyi, “Estimates for sums of moduli of blocks from trigonometric Fourier series”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:4 (2010),  166–179  mathnet  elib; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S190–S204  scopus 5
2009
16. V. P. Zastavnyi, “On Series Arising from the Approximation of Periodic Differentiable Functions by Poisson Integrals”, Mat. Zametki, 86:4 (2009),  497–511  mathnet  mathscinet  zmath; Math. Notes, 86:4 (2009), 469–482  isi  scopus 2
2008
17. V. P. Zastavnyi, “On Zeros of Entire Functions of Special Form”, Mat. Zametki, 83:1 (2008),  24–31  mathnet  mathscinet  zmath  elib; Math. Notes, 83:1 (2008), 23–30  isi  elib  scopus 1
2004
18. V. P. Zastavnyi, “A Theorem on the Zeros of Entire Functions and Its Application”, Mat. Zametki, 75:2 (2004),  192–207  mathnet  mathscinet  zmath; Math. Notes, 75:2 (2004), 175–189  isi 2
2002
19. V. P. Zastavnyi, R. M. Trigub, “Positive-definite splines of special form”, Mat. Sb., 193:12 (2002),  41–68  mathnet  mathscinet  zmath; Sb. Math., 193:12 (2002), 1771–1800  isi  scopus 18
1992
20. V. P. Zastavnyi, “Positive-definite functions that depend on a norm”, Dokl. Akad. Nauk, 325:5 (1992),  901–903  mathnet  mathscinet  zmath; Dokl. Math., 46:1 (1993), 112–114 4

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