Geodesic
Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier--Stieltjes Transform
Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 884-898.

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

The system of exponentials generated by zeros of the Fourier–Stieltjes transform of a finite function with discontinuities at the ends of the support interval $[-a,a]$ is considered in the Lebesgue space on the interval $(-a,a)$ with weight in the form of a finite product of polynomial functions. A sufficient condition, which is unimprovable in a sense, is obtained for the basis property of such a system.
Keywords: system of exponentials, basis property, Riesz basis, Riesz property, Banach space.
Mots-clés : Fourier–Stieltjes transform 
@article{MZM_2014_95_6_a9,
     author = {S. S. Pukhov},
     title = {Bases of {Exponentials} in {Weighted} {Spaces} {Generated} by {Zeros} of the {Fourier--Stieltjes} {Transform}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {884--898},
     publisher = {mathdoc},
     volume = {95},
     number = {6},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a9/}
}
TY  - JOUR
AU  - S. S. Pukhov
TI  - Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier--Stieltjes Transform
JO  - Matematičeskie zametki
PY  - 2014
SP  - 884
EP  - 898
VL  - 95
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a9/
LA  - ru
ID  - MZM_2014_95_6_a9
ER  - 
%0 Journal Article
%A S. S. Pukhov
%T Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier--Stieltjes Transform
%J Matematičeskie zametki
%D 2014
%P 884-898
%V 95
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a9/
%G ru
%F MZM_2014_95_6_a9
S. S. Pukhov. Bases of Exponentials in Weighted Spaces Generated by Zeros of the Fourier--Stieltjes Transform. Matematičeskie zametki, Tome 95 (2014) no. 6, pp. 884-898. http://geodesic.mathdoc.fr/item/MZM_2014_95_6_a9/

[1] R. E. A. C. Paley, N. Wiener, Fourier Transforms in the Complex Domain, Amer. Math. Soc. Colloq. Publ., 19, Amer. Math. Soc., New York, 1934 | MR | Zbl

[2] M. I. Kadets, “Tochnoe znachenie postoyannoi Paleya–Vinera”, Dokl. AN SSSR, 155 (1964), 1253–1254 | MR | Zbl

[3] N. Levinson, Gap and Density Theorems, Amer. Math. Soc., New York, 1940 | MR | Zbl

[4] B. S. Pavlov, “Bazisnost sistemy eksponent i uslovie Makenkhoupta”, Dokl. AN SSSR, 247 (1979), 37–40 | MR | Zbl

[5] S. V. Hruščev, N. K. Nikolskii, B. S. Pavlov, “Unconditional bases of exponentials and of reproducing kernels”, Complex Analysis and Spectral Theory, Lecture Notes in Math., 864, Springer-Verlag, Berlin, 1981, 214–235 | DOI | MR | Zbl

[6] A. M. Minkin, “Otrazhenie pokazatelei i bezuslovnye bazisy iz eksponent”, Algebra i analiz, 3:5 (1991), 109–134 | MR | Zbl

[7] A. M. Sedletskii, “Biortogonalnye razlozheniya funktsii v ryady eksponent na intervalakh veschestvennoi osi”, UMN, 37:5 (1982), 51–95 | MR | Zbl

[8] V. A. Molodenkov, A. P. Khromov, “Razlozhenie po sobstvennym funktsiyam odnoi kraevoi zadachi dlya operatora differentsirovaniya”, Differents. uravneniya i vychislit. matem., 1 (1972), 17–26 | MR | Zbl

[9] R. Hunt, B. Muckenhoupt, R. Wheeden, “Weighted norm inequalities for the conjugate function and Hilbert transform”, Trans. Amer. Math. Soc., 176 (1973), 227–251 | DOI | MR | Zbl

[10] E. I. Moiseev, “O bazisnosti sistem sinusov i kosinusov v vesovom prostranstve”, Differents. uravneniya, 34:1 (1998), 40–44 | MR | Zbl

[11] A. Boivin, A. M. Sedletskii, “Bases of exponentiales in weighted $L^p$-spaces”, Spectral and Evolution Problems, 14, Proc. 14 Crimean Autumn Math. School-Symp. (September 2003, Sevastopol, Laspi), Simferopol, 2004, 41–43

[12] S. S. Pukhov, A. M. Sedletskii, “Bazisy iz eksponent, sinusov i kosinusov v vesovykh prostranstvakh na konechnom intervale”, Dokl. AN SSSR, 425:4 (2009), 452–455 | MR | Zbl

[13] S. S. Pukhov, “Bazisy iz eksponent, sinusov i kosinusov v vesovykh prostranstvakh na konechnom intervale”, Izv. RAN. Ser. matem., 75:2 (2011), 195–224 | DOI | MR | Zbl

[14] A. M. Sedletskii, “Bazisy iz eksponent v vesovykh prostranstvakh, porozhdennye nulyami funktsii tipa sinusa”, Matem. zametki, 89:6 (2011), 894–913 | DOI | MR | Zbl

[15] A. M. Sedletskii, Klassy analiticheskikh preobrazovanii Fure i eksponentsialnye approksimatsii, Fizmatlit, M., 2005

[16] S. S. Pukhov, Bazisy iz eksponent v vesovykh prostranstvakh, porozhdennye nulyami funktsii tipa sinusa spetsialnogo vida, Dep. v VINITI No 724-V2010, M., 2011