Summation methods for Fourier series with respect to the Azoff–Shehada system
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 116-125 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A special class of complete minimal systems with complete biorthogonal system in a Hilbert space is considered. This class was introduced by Azoff and Shehada. The paper studies conditions under which there exists a linear summation method for Fourier series with respect to the Azoff–Shehada system. A construction of a linear summation method of the Fourier series for a given vector is presented, as well as a construction of a universal linear summation method.
@article{ZNSL_2015_434_a9,
     author = {A. Pyshkin},
     title = {Summation methods for {Fourier} series with respect to the {Azoff{\textendash}Shehada} system},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--125},
     year = {2015},
     volume = {434},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a9/}
}
TY  - JOUR
AU  - A. Pyshkin
TI  - Summation methods for Fourier series with respect to the Azoff–Shehada system
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2015
SP  - 116
EP  - 125
VL  - 434
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a9/
LA  - ru
ID  - ZNSL_2015_434_a9
ER  - 
%0 Journal Article
%A A. Pyshkin
%T Summation methods for Fourier series with respect to the Azoff–Shehada system
%J Zapiski Nauchnykh Seminarov POMI
%D 2015
%P 116-125
%V 434
%U http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a9/
%G ru
%F ZNSL_2015_434_a9
A. Pyshkin. Summation methods for Fourier series with respect to the Azoff–Shehada system. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 43, Tome 434 (2015), pp. 116-125. http://geodesic.mathdoc.fr/item/ZNSL_2015_434_a9/

[1] L. N. Dovbysh, N. K. Nikolskii, V. N. Sudakov, “Naskolko khoroshim mozhet byt nenasledstvenno polnoe semeistvo?”, Zap. nauchn. sem. LOMI, 73, 1977, 52–69 | MR | Zbl

[2] L. N. Dovbysh, N. K. Nikolskii, “Dva sposoba izbezhat nasledstvennoi polnoty”, Zap. nauchn. sem. LOMI, 65, 1976, 183–188 | MR | Zbl

[3] A. S. Markus, “Zadacha spektralnogo sinteza dlya operatorov s tochechnym spektrom”, Izv. AN SSSR. Ser. matem., 34:3 (1970), 662–668 | MR | Zbl

[4] N. K. Nikolskii, “Polnye rasshireniya volterrovykh operatorov”, Izv. AN SSSR. Ser. matem., 33:6 (1969), 1349–1355 | MR | Zbl

[5] E. Azoff, H. Shehada, “Algebras generated by mutually orthogonal idempotent operators”, J. Oper. Theory, 29:2 (1993), 249–267 | MR | Zbl

[6] A. Baranov, Yu. Belov, A. Borichev, “Hereditary completeness for systems of exponentials and reproducing kernels”, Adv. Math., 235:1 (2013), 525–554 | DOI | MR | Zbl

[7] A. Baranov, Yu. Belov, A. Borichev, “Spectral synthesis in de Branges spaces”, Geom. Funct. Anal. (GAFA), 25:2 (2015), 417–452 | DOI | MR | Zbl

[8] A. D. Baranov, D. V. Yakubovich, Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators, arXiv: 1212.5965[math.FA]

[9] A. Katavolos, M. Lambrou, M. Papadakis, “On some algebras diagonalized by $M$-bases of $\ell^2$”, Integr. Equat. Oper. Theory, 17:1 (1993), 68–94 | DOI | MR | Zbl

[10] D. Larson, W. Wogen, “Reflexivity properties of $T\bigoplus0$”, J. Funct. Anal., 92 (1990), 448–467 | DOI | MR | Zbl