Geodesic
Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts
Algebra i analiz, Tome 30 (2018) no. 5, pp. 112-148.

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

@article{AA_2018_30_5_a3,
     author = {O. L. Vinogradov},
     title = {Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts},
     journal = {Algebra i analiz},
     pages = {112--148},
     publisher = {mathdoc},
     volume = {30},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2018_30_5_a3/}
}
TY  - JOUR
AU  - O. L. Vinogradov
TI  - Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts
JO  - Algebra i analiz
PY  - 2018
SP  - 112
EP  - 148
VL  - 30
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2018_30_5_a3/
LA  - ru
ID  - AA_2018_30_5_a3
ER  - 
%0 Journal Article
%A O. L. Vinogradov
%T Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts
%J Algebra i analiz
%D 2018
%P 112-148
%V 30
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2018_30_5_a3/
%G ru
%F AA_2018_30_5_a3
O. L. Vinogradov. Sharp constants for approximations of convolution classes with an integrable kernel by spaces of shifts. Algebra i analiz, Tome 30 (2018) no. 5, pp. 112-148. http://geodesic.mathdoc.fr/item/AA_2018_30_5_a3/

[1] Favard J., “Sur les meilleurs procédés d'approximation de certaines classes des fonctions par des polynomes trigonométriques”, Bull. Sci. Math., 61 (1937), 209–224, 243–256 | MR | Zbl

[2] Akhiezer N. I., Krein M. G., “O nailuchshem priblizhenii trigonometricheskimi summami differentsiruemykh periodicheskikh funktsii”, Dokl. AN SSSR, 15:3 (1937), 107–112

[3] Nikolskii S. M., “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR. Ser. mat., 10:3 (1946), 207–256 | MR | Zbl

[4] Korneichuk N. P., Tochnye konstanty v teorii priblizheniya, Nauka, M., 1987 | MR

[5] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1965

[6] Pinkus P., $N$-widths in approximation theory, Ergeb. Math. Grenzgeb. (3), 7, Springer-Verlag, Berlin, 1985 | MR | Zbl

[7] Babenko V. F., “Ekstremalnye zadachi teorii priblizheniya i neravenstva dlya perestanovok”, Dokl. AN SSSR, 290:5 (1986), 1033–1036 | MR

[8] Babenko V. F., “Priblizhenie klassov svertok”, Sib. mat. zh., 28:5 (1987), 6–21 | MR | Zbl

[9] Tikhomirov V. M., “Ob ekstremalnykh podprostranstvakh dlya klassov funktsii, zadavaemykh yadrami, ne povyshayuschimi ostsillyatsiyu”, Vestn. Mosk. un-ta. Ser. 1. Mat. Mekh., 1997, no. 4, 16–19 | Zbl

[10] Ligun A. A., “Inequalities for upper bounds of functionals”, Anal. Math., 2:1 (1976), 11–40 | DOI | MR | Zbl

[11] Vinogradov O. L., “Analog summ Akhiezera–Kreina–Favara dlya periodicheskikh splainov minimalnogo defekta”, Probl. mat. anal., 25, 2003, 29–56 | Zbl

[12] Vinogradov O. L., “Tochnye neravenstva dlya priblizhenii klassov svertok periodicheskikh funktsii podprostranstvami sdvigov nechetnoi razmernosti”, Mat. zametki, 85:4 (2009), 569–584 | DOI | MR | Zbl

[13] Krein M. G., “O nailuchshei approksimatsii nepreryvnykh differentsiruemykh funktsii na vsei veschestvennoi osi”, Dokl. AN SSSR, 18:9 (1938), 619–623

[14] Vinogradov O. L., “Tochnye neravenstva tipa Dzheksona dlya priblizhenii klassov svertok tselymi funktsiyami konechnoi stepeni”, Algebra i analiz, 17:4 (2005), 56–114 | MR | Zbl

[15] Vinogradov O. L., “Tochnye neravenstva dlya priblizhenii klassov svertok na osi kak predelnyi sluchai neravenstv dlya periodicheskikh svertok”, Sib. mat. zh., 58:2 (2017), 251–269 | DOI | MR | Zbl

[16] Vinogradov O. L., Gladkaya A. V., “Neperiodicheskii splainovyi analog operatorov Akhiezera–Kreina–Favara”, Zap. nauch. semin. POMI, 440, 2015, 8–35 | MR

[17] Buhmann M. D., “Multivariate cardinal interpolation with radial-basis functions”, Constr. approx., 6:3 (1990), 225–255 | DOI | MR | Zbl

[18] Ron A., “Introduction to shift-invariant spaces. Linear independence”, Multivariate approximation and applications, Cambridge Univ. Press, Cambridge, 2001, 112–151 | DOI | MR | Zbl

[19] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2005

[20] Schoenberg I. J., Cardinal spline interpolation, SBMS Reg. Conf. Ser. Appl. Math., 12, Soc. Industr. Appl. Math., Philadelphia, Pa, 1973 | MR | Zbl

[21] Magaril-Ilyaev G. G., “Srednyaya razmernost, poperechniki i optimalnoe vosstanovlenie sobolevskikh klassov funktsii na pryamoi”, Mat. sb., 182:11 (1991), 1635–1656 | MR | Zbl

[22] Makarov B. M., Podkorytov A. N., Lektsii po veschestvennomu analizu, BKhV-Peterburg, SPb., 2011 | MR

[23] Kloos T., “Zeros of the Zak transform of totally positive functions”, J. Fourier Anal. Appl., 21:5 (2015), 1130–1145 | DOI | MR | Zbl

[24] Zigmund A., Trigonometricheskie ryady, v. 1, Mir, M., 1965 | MR

[25] Karlin S., Total positivity, v. 1, Stanford Univ. Press, Stanford, 1968 | MR | Zbl

[26] Lorentz G. G., DeVore R. A., Constructive approximation, Grundlehren Math. Wiss., 303, Springer-Verlag, Berlin, 1993 | MR | Zbl

[27] Jetter K., Riemenschneider S. D., Sivakumar N., “Schoenberg's exponential Euler spline curves”, Proc. Roy. Soc. Edinburgh Sect. A, 118:1–2 (1991), 21–33 | DOI | MR | Zbl

[28] Baxter B. J. C., Sivakumar N., “On shifted cardinal interpolation by Gaussians and multiquadrics”, J. Approx. Theory, 87:1 (1996), 36–59 | DOI | MR | Zbl

[29] Vinogradov O. L., Ulitskaya A. Yu., “Zeros of the Zak transform of averaged totally positive functions”, J. Approx. Theory, 222 (2017), 55–63 | DOI | MR | Zbl