Analogs of Lorentz theorems for double multiplicative systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 76-85.

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

In this paper we prove Lorentz-type theorems connecting the behavior of Fourier coefficients and the decreasing order of the mixed modulus of continuity for double multiplicative systems with a bounded generating sequence.
Keywords: double multiplicative systems, Lorentz-type theorems, mixed modulus of continuity, generalized monotonicity.
@article{IVM_2012_2_a8,
     author = {R. N. Fadeev},
     title = {Analogs of {Lorentz} theorems for double multiplicative systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {76--85},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_2_a8/}
}
TY  - JOUR
AU  - R. N. Fadeev
TI  - Analogs of Lorentz theorems for double multiplicative systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2012
SP  - 76
EP  - 85
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2012_2_a8/
LA  - ru
ID  - IVM_2012_2_a8
ER  - 
%0 Journal Article
%A R. N. Fadeev
%T Analogs of Lorentz theorems for double multiplicative systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2012
%P 76-85
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2012_2_a8/
%G ru
%F IVM_2012_2_a8
R. N. Fadeev. Analogs of Lorentz theorems for double multiplicative systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2012), pp. 76-85. http://geodesic.mathdoc.fr/item/IVM_2012_2_a8/

[1] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha. Teoriya i primeneniya, Nauka, M., 1987 | MR | Zbl

[2] Lorentz G. G., “Fourier-Koeffizienten und Funktionenklassen”, Math. Z., 51:2 (1948), 135–149 | DOI | MR | Zbl

[3] Bari N. K., Trigonometricheskie ryady, Fizmatgiz, M., 1961 | MR

[4] Kagadii L. P., “Klassy funktsii $\Lambda_p(\alpha,\beta)$ i koeffitsienty Fure”, Ukr. matem. zhurn., 26:3 (1974), 367–374 | MR | Zbl

[5] Agaev G. N., Vilenkin N. Ya., Dzhafarli G. M., Rubinshtein A. I., Multiplikativnye sistemy funktsii i garmonicheskii analiz na nul-mernykh gruppakh, Elm, Baku, 1981

[6] Aljancić S., Tomić M., “Über den Stetigkeitsmodul von Fourier-Reihen mit monotonen Koeffizienten”, Math. Z., 88:3 (1965), 274–284 | DOI | MR | Zbl

[7] Volosivets C. S., “Skhodimost ryadov Fure po multiplikativnym sistemam i $p$-fluktuatsionnyi modul nepreryvnosti”, Sib. matem. zhurn., 47:2 (2006), 241–258 | MR | Zbl

[8] Kagadii L. P., “Koeffitsienty Fure i moduli gladkosti funktsii dvukh peremennykh”, Uchen. zap. Tartusk. un-ta, 253:9 (1970), 229–243 | MR | Zbl