D. V. Prokhorov, “Sets of values of systems of functionals in classes of univalent functions”, Math. USSR-Sb., 71:2 (1992), 499

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Mathematics of the USSR-Sbornik, 1992, Volume 71, Issue 2, Pages 499–516
DOI: https://doi.org/10.1070/SM1992v071n02ABEH001407 (Mi sm1253)

This article is cited in 16 scientific papers (total in 16 papers)

Sets of values of systems of functionals in classes of univalent functions

D. V. Prokhorov

Saratov State University named after N. G. Chernyshevsky

English version PDF (1052 kB) Citations (16) Russian version article

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DOI: https://doi.org/10.1070/SM1992v071n02ABEH001407

Abstract: The problem of describing the set of values of a system of functional

$\{f(z),\dots,f^{(n)}(z)\}$ in the class of univalent functions holomorphic in the disk is formalized as a problem of constructing the set of attainability for a control system generated by the Löwner equation. In this problem the maximum principle turns out to be a necessary and sufficient condition for optimality. An algorithm for finding this set for a generalized Loewner equation with constant coefficients and continuous control is constructed. The results are extended to classes of bounded univalent functions.

Received: 26.09.1989

Bibliographic databases:

UDC: 517.546.1+517.977.5

MSC: Primary 30C55, 34H05, 93B03; Secondary 30C45

Language: English

Original paper language: Russian

Citation: D. V. Prokhorov, “Sets of values of systems of functionals in classes of univalent functions”, Math. USSR-Sb., 71:2 (1992), 499–516

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/sm1253

https://doi.org/10.1070/SM1992v071n02ABEH001407

https://www.mathnet.ru/eng/sm/v181/i12/p1659

This publication is cited in the following 16 articles:

F. G. Avkhadiev, I. R. Kayumov, S. R. Nasyrov, “Extremal problems in geometric function theory”, Russian Math. Surveys, 78:2 (2023), 211–271
D. V. Prokhorov, “Value regions in classes of conformal mappings”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 19:3 (2019), 258–279
A. V. Zherdev, “Value range of solutions to the chordal Loewner equation with restriction on the driving function”, Probl. anal. Issues Anal., 8(26):2 (2019), 92–104
D. Prokhorov, “Qualitative Results in the Bombieri Problem for Conformal Mappings”, Lobachevskii J Math, 40:9 (2019), 1397
Dmitri Prokhorov, “Necessary criteria for the Bombieri conjecture”, Anal.Math.Phys., 8:4 (2018), 679
V. G. Gordienko, K. A. Samsonova, “Opredelenie granitsy v lokalnoi gipoteze Khazhinskogo–Tammi dlya pyatogo koeffitsienta”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 13:4(1) (2013), 5–14
D. V. Prokhorov, V. G. Gordienko, “Definition of a boundary in the local Charzyński-Tammi conjecture”, Russian Math. (Iz. VUZ), 52:9 (2008), 51–59
D. V. Prokhorov, A. A. Nikulin, “Asymptotic estimates for the coefficients of bounded univalent functions”, Siberian Math. J., 47:5 (2006), 924–933
Dmitri Prokhorov, Alexander Vasil'ev, “Univalent Functions and Integrable Systems”, Commun. Math. Phys., 262:2 (2006), 393
D.V. Prokhorov, “Extremal Bounded Slit Mappings for Linear Functionals”, Rocky Mountain J. Math., 33:3 (2003)
D.V. Prokhorov, Handbook of Complex Analysis, 1, Geometric Function Theory, 2002, 207
G. N. Kamyshova, “A variational method and optimal control in the solution of the Mocanu problem”, Russian Math. (Iz. VUZ), 42:8 (1998), 33–40
I. R. Kayumov, “On an extremal problem in airfoil theory”, Russian Math. (Iz. VUZ), 42:11 (1998), 39–44
D. V. Prokhorov, “The sum of coefficients of bounded univalent functions”, Math. Notes, 61:5 (1997), 609–613
Dmitri Prokhorov, “Coefficients of Functions Close to the Identity Function”, Complex Variables, Theory and Application: An International Journal, 33:1-4 (1997), 255
D. V. Prokhorov, “Coefficient products for bounded univalent functions”, Complex Variables, Theory and Application: An International Journal, 27:3 (1995), 211

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	510
Russian version PDF:	194
English version PDF:	26
References:	81
First page:	1

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