Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MZM_2006_80_5_a6, author = {D. V. Gorbachev and S. A. Strankovskii}, title = {An extremal problem for even positive definite entire functions of exponential type}, journal = {Matemati\v{c}eskie zametki}, pages = {712--717}, publisher = {mathdoc}, volume = {80}, number = {5}, year = {2006}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a6/} }
TY - JOUR AU - D. V. Gorbachev AU - S. A. Strankovskii TI - An extremal problem for even positive definite entire functions of exponential type JO - Matematičeskie zametki PY - 2006 SP - 712 EP - 717 VL - 80 IS - 5 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a6/ LA - ru ID - MZM_2006_80_5_a6 ER -
D. V. Gorbachev; S. A. Strankovskii. An extremal problem for even positive definite entire functions of exponential type. Matematičeskie zametki, Tome 80 (2006) no. 5, pp. 712-717. http://geodesic.mathdoc.fr/item/MZM_2006_80_5_a6/
[1] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR | Zbl
[2] G. Beitmen, A. Erdeii, Vysshie transtsendentnye funktsii, t. 2, Nauka, M., 1966 | MR
[3] B. M. Levitan, I. S. Sargsyan, Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR | Zbl
[4] D. V. Gorbachev, Izbrannye zadachi teorii funktsii i teorii priblizhenii i ikh prilozheniya, TulGU, Tula, 2004
[5] N. I. Chernykh, “O neravenstve Dzheksona v $L_2$”, Tr. MIAN, 88, 1967, 71–74
[6] B. F. Logan, “Extremal problems for positive-definite bandlimited functions. II. Eventually negative functions”, SIAM J. Math. Anal., 14:2 (1983), 253–257 | DOI | MR | Zbl
[7] V. A. Yudin, “Mnogomernaya teorema Dzheksona v $L_2$”, Matem. zametki, 29:2 (1981), 309–315 | MR | Zbl
[8] A. V. Moskovskii, “Teoremy Dzheksona v prostranstvakh $L_p(\mathbb{R}^n)$ i $L_{p,\lambda}(\mathbb{R}_{+})$”, Izv. TulGU. Ser. matem., 3:1 (1997), 44–70 | MR
[9] A. G. Babenko, “Tochnoe neravenstvo Dzheksona–Stechkina v prostranstve $L^2(\mathbb R^m)$”, Tr. IMM UrO RAN, 5 (1998), 183–198 | Zbl
[10] N. I. Chernykh, V. V. Arestov, “On the $L_2$-approximation of periodic functions by trigonometric polynomials”, Approximation and Function Spaces, Proc. Inter. Conf. (Gdansk, 1979), North-Holland, Amsterdam, 1981, 25–43 | MR | Zbl
[11] V. V. Arestov, A. G. Babenko, “On the optimal point in Jackson's inequality in $L^2(-\infty,\infty)$ with the second modulus of continuity”, East J. Approximation, 10:1–2 (2004), 201–214 | MR | Zbl
[12] A. G. Babenko, Pryamye teoremy teorii priblizheniya v $L^2$ i rodstvennye ekstremalnye zadachi dlya polozhitelno opredelennykh funktsii, Diss. ... d.f.-m.n., Ekaterinburg, 2004
[13] E. E. Berdysheva, “Dve vzaimosvyazannye ekstremalnye zadachi dlya tselykh funktsii mnogikh peremennykh”, Matem. zametki, 66:3 (1999), 336–350 | MR | Zbl
[14] E. E. Berdysheva, “An extremal problem for entire functions of exponential type with non-negative mean value”, East J. Approximation, 3:4 (1997), 393–401 | MR | Zbl
[15] N. I. Chernykh, “O nailuchshem priblizhenii periodicheskikh funktsii trigonometricheskimi polinomami v $L_2$”, Matem. zametki, 2:5 (1967), 513–522
[16] S. N. Vasilev, Approksimatsiya funktsii trigonometricheskimi polinomami v $L^2$ i fraktalnymi funktsiyami v $C$, Diss. ... k.f.-m.n., Ekaterinburg, 2002