On some properties of sinc approximations of continuous functions on the interval
Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 111-126 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study approximation properties of various operators being the modifications of sinc approximations of continuous functions on an interval.
Keywords: sinc approximation, interpolation functions, uniform approximation.
@article{UFA_2015_7_4_a10,
     author = {A. Yu. Trynin},
     title = {On some properties of sinc approximations of continuous functions on the interval},
     journal = {Ufa mathematical journal},
     pages = {111--126},
     year = {2015},
     volume = {7},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a10/}
}
TY  - JOUR
AU  - A. Yu. Trynin
TI  - On some properties of sinc approximations of continuous functions on the interval
JO  - Ufa mathematical journal
PY  - 2015
SP  - 111
EP  - 126
VL  - 7
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a10/
LA  - en
ID  - UFA_2015_7_4_a10
ER  - 
%0 Journal Article
%A A. Yu. Trynin
%T On some properties of sinc approximations of continuous functions on the interval
%J Ufa mathematical journal
%D 2015
%P 111-126
%V 7
%N 4
%U http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a10/
%G en
%F UFA_2015_7_4_a10
A. Yu. Trynin. On some properties of sinc approximations of continuous functions on the interval. Ufa mathematical journal, Tome 7 (2015) no. 4, pp. 111-126. http://geodesic.mathdoc.fr/item/UFA_2015_7_4_a10/

[1] F. Stenger, Numerical Metods Based on Sinc and Analytic Functions, Springer Ser. Comput. Math., 20, Springer-Verlag, N.Y., 1993 | DOI | MR

[2] P. L. Butzer, “A retrospective on 60 years of approximation theory and associated fields”, Journal of Approximation Theory, 160 (2009), 3–18 | DOI | MR | Zbl

[3] J. R. Higgins, “Five short stories about the cardinal series”, Bulletin (New Series) Of the american mathematical society, 12:1 (1985), 45–89 | DOI | MR | Zbl

[4] M. T. Alquran, K. Al-Khaled, “Numerical Comparison of Methods for Solving Systems of Conservation Laws of Mixed Type”, Int. Journal of Math. Analysis, 5:1 (2011), 35–47 | MR | Zbl

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

[6] Dobeshi I., Desyat lektsii po veivletam, “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001

[7] Novikov I. Ya., Stechkin S. B., “Osnovnye konstruktsii vspleskov”, Fundamentalnaya i prikladnaya matematika, 3:4 (1997), 999–1028 | MR | Zbl

[8] Novikov I. Ya., Stechkin S. B., “Osnovy teorii vspleskov”, Uspekhi matematicheskikh nauk, 53:6(324) (1998), 53–128 | DOI | MR | Zbl

[9] J. L. Brown (Jr.), “On the error in reconstructing a nonbandlimited function by means of bandpass sampling theorem”, J. of Mathematical Analysis and Applications, 18 (1967), 75–84 | DOI | MR | Zbl

[10] P. L. Butzer, J. R. Higgins, R. L. Stens, “Classical and approximate sampling theorems: studies in the $L^p(\mathbb R)$ and the uniform norm”, Journal of Approximation Theory, 137 (2005), 250–263 | DOI | MR | Zbl

[11] Shmukler A. I., Shulman T. A., “O nekotorykh svoistvakh ryadov Kotelnikova”, Izvestiya vuzov. Matematika, 1974, no. 3, 93–103 | MR | Zbl

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

[13] A. Kivinukk, G. Tamberg, “On Blackman–Harris windows for Shannon sampling series”, Sampl. Theory Signal Image Process., 6 (2007), 87–108 | MR | Zbl

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

[15] G. Schmeisser, “Interconnections Between Multiplier Methods and Window Methods in Generalized Sampling”, Sampl. Theory Signal Image Process., 9:1–3 (2010), 1–24 | MR | Zbl

[16] Abdul J. Jerri, “Lanczos-Like $\sigma$-Factors for Reducing the Gibbs Phenomenon in General Orthogonal Expansions and Other Representations”, Journal of Computational Analysis and Applications, 2:2 (2000), 111–127 | DOI | MR | Zbl

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

[18] Trynin A. Yu., “Ob approksimatsii analiticheskikh funktsii operatorami Lagranzha–Shturma–Liuvillya”, Tezisy dokladov X Saratovskoi zimnei shkoly “Sovremennye problemy teorii funktsii i ikh prilozheniya” (27 yanvarya – 2 fevralya 2000 g.), Izd-vo Sarat. un-ta, Saratov, 140–141

[19] Trynin A. Yu., “Ob otsenke approksimatsii analiticheskikh funktsii interpolyatsionnym operatorom po sinkam”, Matematika. Mekhanika, 7, Izd-vo Sarat. un-ta, Saratov, 2005, 124–127

[20] Trynin A. Yu., “Otsenki funktsii Lebega i formula Nevai dlya sinc-priblizhenii nepreryvnykh funktsii na otrezke”, Sibirskii matematicheskii zhurnal, 48:5 (2007), 1155–1166 | MR | Zbl

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

[22] Trynin A. Yu., “Kriterii ravnomernoi skhodimosti sinc-priblizhenii na otrezke”, Izvestiya vyssh. uch-ykh zavedenii. Matematika, 2008, no. 6, 66–78 | MR | Zbl

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

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

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

[26] 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

[27] Trynin A. Yu., “Ob otsutstvii ustoichivosti interpolirovaniya po sobstvennym funktsiyam zadachi Shturma–Liuvillya”, Izvestiya vyssh. uch-ykh zavedenii. Matematika, 2000, no. 9(460), 60–73 | MR | Zbl

[28] Trynin A. Yu., “O raskhodimosti interpolyatsionnykh protsessov Lagranzha po sobstvennym funktsiyam zadachi Shturma–Liuvillya”, Izvestiya vyssh. uch-ykh zavedenii. Matematika, 2010, no. 11, 74–85 | MR | Zbl

[29] 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

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

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

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

[33] Polovinkin E. S., “Ob integrirovanii mnogoznachnykh otobrazhenii”, DAN, 281:5 (1983), 1069–1074 | MR

[34] Borisov D. I., Gadylshin R. R., “O spektre periodicheskogo operatora s malym lokalizovannym vozmuscheniem”, Izv. RAN. Ser. matem., 72:4 (2008), 37–66 | DOI | MR | Zbl

[35] Borisov D. I., Gadylshin R. R., “O spektre samosopryazhennogo differentsialnogo operatora na osi s bystro ostsilliruyuschimi koeffitsientami”, Matem. sb., 198:8 (2007), 3–34 | DOI | MR | Zbl

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

[37] Bernshtein S. N., “Ob odnom vidoizmenenii interpolyatsionnoi formuly Lagranzha”, Sobranie sochinenii, v. 2, Konstruktivnaya teoriya funktsii, Izd-vo AN SSSR, M., 1954, 130–140

[38] Daugavet I. K., Vvedenie v teoriyu priblizheniya funktsii, Izd-vo Leningradskogo universiteta, Leningrad, 1977 | MR

[39] Karlin S., Stadden V., Chebyshevskie sistemy i ikh primenenie v analize i statistike, “Nauka”, Glavn. red. fiziko-matematicheskoi literatury, M., 1976 | MR

[40] Prudnikov A. P., Brychkov Yu. A., Marichev O. I., Integraly i ryady, “Nauka”, Glavn. red. fiziko-matematicheskoi literatury, M., 1981 | MR

[41] Lyusternik L. A., Sobolev V. I., Elementy funktsionalnogo analiza, “Nauka”, Glavn. red. fiziko-matematicheskoi literatury, M., 1965 | MR