Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2013_25_6_a4, author = {L. S. Maergoiz and N. N. Rybakova}, title = {Chebyshev polynomials with zeros on a~circle and adjacent problems}, journal = {Algebra i analiz}, pages = {103--124}, publisher = {mathdoc}, volume = {25}, number = {6}, year = {2013}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2013_25_6_a4/} }
L. S. Maergoiz; N. N. Rybakova. Chebyshev polynomials with zeros on a~circle and adjacent problems. Algebra i analiz, Tome 25 (2013) no. 6, pp. 103-124. http://geodesic.mathdoc.fr/item/AA_2013_25_6_a4/
[1] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949
[2] Ivanov V. K., “Zadacha o minimakse sistemy lineinykh funktsii”, Mat. sb., 28(70):3 (1951), 685–706 | MR | Zbl
[3] Lavrentev M. M., O nekotorykh nekorrektnykh zadachakh matematicheskoi fiziki, Izd-vo SO AN SSSR, Novosibirsk, 1962 | MR
[4] Thiran J. P., Detaille C., “Chebyshev polynomials on circular arcs in the complex plane”, Progress in Approximation Theory, Acad. Press, Boston, MA, 1991, 771–786 | MR
[5] Goluzin G. M., Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl
[6] Tyshkevich S. V., “O chebyshevskikh polinomakh na dugakh okruzhnosti”, Mat. zametki, 81:6 (2007), 952–954 | DOI | MR | Zbl
[7] Maergoiz L. S., Rybakova N. N., Mnogochleny Chebysheva s nulyami na okruzhnosti i smezhnye voprosy, Preprint, Sibirskii federalnyi un-t, Krasnoyarsk, 2012, 28 pp.
[8] Smirnov V. I., Lebedev N. A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M.–L., 1964 | MR
[9] Goncharov V. L., Teoriya interpolirovaniya i priblizheniya funktsii, GITTL, M., 1954
[10] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR | Zbl
[11] Maergoiz L. S., “Polinomy Chebysheva s nulyami na zadannom kompakte i ikh prilozheniya”, Kompleksnyi analiz i ego prilozheniya, Tez. dokl. Mezhdunar. shk.-konf., posvyaschennoi pamyati prof. I. P. Mityuka (11–17 sentyabrya 2005 g.), Izd-vo Krasnodar. un-ta, Krasnodar, 2005, 75–76
[12] Videnskii V. S., “Ekstremalnye otsenki proizvodnoi trigonometricheskogo polinoma na otrezke, menshem chem period”, Dokl. AN SSSR, 130:1 (1960), 13–16 | MR
[13] Timan A. F., Teoriya priblizheniya funktsii deistvitelnogo peremennogo, Gos. izd-vo fiz.-mat. lit., M., 1960
[14] Maergoiz L. S., Rybakova N. N., “Mnogochleny Chebysheva s nulevym mnozhestvom na duge okruzhnosti”, Algoritmicheskii analiz neustoichivykh zadach, Tez. dokl. Mezhdunar. konf., posvyaschennoi 100-letiyu so dnya rozhdeniya V. K. Ivanova (1–6 sentyabrya 2008 g.), Izd-vo Uralskogo un-ta, Ekaterinburg, 2008, 73–74
[15] Maergoiz L. S., Rybakova N. N., “Mnogochleny Chebysheva s nulevym mnozhestvom na duge okruzhnosti”, Dokl. RAN, 426:1 (2009), 26–28 | MR | Zbl
[16] Maergoiz L. S., Rybakova N. N., Mnogochleny Chebysheva s nulevym mnozhestvom na duge okruzhnosti i smezhnye voprosy, Preprint 312M, In-t fiziki im. L. V. Kirenskogo SO RAN, Krasnoyarsk, 2008, 16 pp.
[17] Lukashov A. L., Tyshkevich S. V., “Ekstremalnye polinomy na dugakh okruzhnosti s nulyami na etikh dugakh”, Izv. NAN Armenii. Mat., 44:3 (2009), 19–29 | MR
[18] Marchuk A. G., Osipenko K. Yu., “Nailuchshee priblizhenie funktsii, zadannykh s pogreshnostyu v konechnom chisle tochek”, Mat. zametki, 17:3 (1975), 359–368 | MR | Zbl
[19] Maergoiz L. S., “Optimalnaya oshibka ekstrapolyatsii s konechnogo mnozhestva v klasse Vinera”, Sib. mat. zh., 41:6 (2000), 1363–1375 | MR | Zbl
[20] Arestov V. V., Mendelev A. S., “Trigonometric polynomials of least deviation from zero in measure and related problems”, J. Approx. Theory, 162:10 (2010), 1852–1878 | DOI | MR | Zbl
[21] Olesov A. V., “O primenenii konformnykh otobrazhenii k neravenstvam dlya trigonometricheskikh polinomov”, Mat. zametki, 76:3 (2004), 396–408 | DOI | MR | Zbl
[22] Schiefermayr K., “Geometric properties of inverse polynomial images”, Proc. Approximation Theory XIII (San Antonio, 2010), Proc. in Mathematics, 13, Springer, 2012, 277–287 | MR | Zbl