Approximation of continuous on a~segment functions with the help of linear combinations of sincs
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 72-81.

Voir la notice de l'article provenant de la source Math-Net.Ru

We investigate approximate properties of various operators, which are modifications of sinc-approximations of continuous functions on the segment.
Keywords: sinc-approximation, interpolation of functions, uniform approximation.
@article{IVM_2016_3_a7,
     author = {A. Yu. Trynin},
     title = {Approximation of continuous on a~segment functions with the help of linear combinations of sincs},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--81},
     publisher = {mathdoc},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_3_a7/}
}
TY  - JOUR
AU  - A. Yu. Trynin
TI  - Approximation of continuous on a~segment functions with the help of linear combinations of sincs
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 72
EP  - 81
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_3_a7/
LA  - ru
ID  - IVM_2016_3_a7
ER  - 
%0 Journal Article
%A A. Yu. Trynin
%T Approximation of continuous on a~segment functions with the help of linear combinations of sincs
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 72-81
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_3_a7/
%G ru
%F IVM_2016_3_a7
A. Yu. Trynin. Approximation of continuous on a~segment functions with the help of linear combinations of sincs. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 72-81. http://geodesic.mathdoc.fr/item/IVM_2016_3_a7/

[1] Kashin B. S., Saakyan A. A., Ortogonalnye ryady, Izd-vo AFTs, M., 1999 | MR

[2] Novikov I. Ya., Stechkin S. B., “Osnovy teorii vspleskov”, UMN, 53:6 (1998), 53–128 | DOI | MR | Zbl

[3] Sklyarov V. P., “On the best uniform sinc-approximation on a finite interval”, East J. Approx., 14:2 (2008), 183–192 | MR | Zbl

[4] Kivinukk A., Tamberg G., “Interpolating generalized Shannon sampling operators, their norms and approximation properties”, Sampl. Theory Signal Image Process., 8:1 (2009), 77–95 | MR | Zbl

[5] Schmeisser G., “Interconnections between multiplier methods and window methods in generalized sampling”, Sampl. Theory Signal Image Process., 9:1–3 (2010), 1–24 | MR | Zbl

[6] Trynin A. Yu., Sklyarov V. P., “Error of sinc approximation of analytic functions on an interval”, Sampl. Theory Signal and Image Process., 7:3 (2008), 263–270 | MR | Zbl

[7] Trynin A.Yu., “Otsenki funktsii Lebega i formula Nevai dlya $\mathrm{sinc}$-priblizhenii nepreryvnykh funktsii na otrezke”, Sib. matem. zhurn., 48:5 (2007), 1155–1166 | MR | Zbl

[8] Trynin A. Yu., “Kriterii potochechnoi i ravnomernoi skhodimosti sink-priblizhenii nepreryvnykh funktsii na otrezke”, Matem. sb., 198:10 (2007), 141–158 | DOI | MR | Zbl

[9] Trynin A. Yu., “Kriterii ravnomernoi skhodimosti sinc-priblizhenii na otrezke”, Izv. vuzov. Matem., 2008, no. 6, 66–78 | MR | Zbl

[10] Livne Oren E., Brandt Achi E., “MuST: The multilevel sinc transform”, SIAM J. Sci. Comput., 33:4 (2011), 1726–1738 | DOI | MR | Zbl

[11] Trynin A. Yu., “O raskhodimosti sink-priblizhenii vsyudu na $(0,\pi)$”, Algebra i analiz, 22:4 (2010), 232–256 | MR | Zbl

[12] Trynin A. Yu., “Obobschenie teoremy otschetov Uittekera–Kotelnikova–Shennona dlya nepreryvnykh funktsii na otrezke”, Matem. sb., 200:11 (2009), 61–108 | DOI | MR | Zbl

[13] Trynin A. Yu., “Ob operatorakh interpolirovaniya po resheniyam zadachi Koshi i mnogochlenakh Lagranzha–Yakobi”, Izv. RAN. Ser. matem., 75:6 (2011), 129–162 | DOI | MR | Zbl

[14] Trynin A. Yu., “Ob otsutstvii ustoichivosti interpolirovaniya po sobstvennym funktsiyam zadachi Shturma–Liuvillya”, Izv. vuzov. Matem., 2000, no. 9, 60–73 | MR | Zbl

[15] Trynin A. Yu., “O raskhodimosti interpolyatsionnykh protsessov Lagranzha po sobstvennym funktsiyam zadachi Shturma–Liuvillya”, Izv. vuzov. Matem., 2010, no. 11, 74–85 | MR | Zbl

[16] Golubov B. I., “Ob absolyutnoi skhodimosti kratnykh ryadov Fure”, Matem. zametki, 37:1 (1985), 13–24 | MR | Zbl

[17] Golubov B. I., “Sfericheskii skachok funktsii i srednie Bokhnera–Rissa sopryazhennykh kratnykh ryadov i integralov Fure”, Matem. zametki, 91:4 (2012), 506–514 | DOI | MR | Zbl

[18] Dyachenko M. I., “Ob odnom klasse metodov summirovaniya kratnykh ryadov Fure”, Matem. sb., 204:3 (2013), 3–18 | DOI | MR | Zbl

[19] Dyachenko M. I., “Ravnomernaya skhodimost giperbolicheskikh chastichnykh summ kratnykh ryadov Fure”, Matem. zametki, 76:5 (2004), 723–731 | DOI | MR | Zbl

[20] Polovinkin E. S., “O nekotorykh svoistvakh proizvodnykh mnogoznachnykh otobrazhenii”, Tr. MFTI, 4:4 (2012), 141–154 | MR

[21] Skopina M. A., “Ortogonalnye polinomialnye bazisy Shaudera v $C[-1,1]$ s optimalnym rostom stepenei”, Matem. sb., 192:3 (2001), 115–136 | DOI | MR | Zbl

[22] Natanson I. P., Konstruktivnaya teoriya funktsii, GITTL, M.–L., 1949