Geodesic
Operators of the multiplicative Fourier transform
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2006), pp. 9-23.

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

@article{IVM_2006_3_a1,
     author = {M. S. Bespalov},
     title = {Operators of the multiplicative {Fourier} transform},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {9--23},
     publisher = {mathdoc},
     number = {3},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2006_3_a1/}
}
TY  - JOUR
AU  - M. S. Bespalov
TI  - Operators of the multiplicative Fourier transform
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2006
SP  - 9
EP  - 23
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2006_3_a1/
LA  - ru
ID  - IVM_2006_3_a1
ER  - 
%0 Journal Article
%A M. S. Bespalov
%T Operators of the multiplicative Fourier transform
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2006
%P 9-23
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2006_3_a1/
%G ru
%F IVM_2006_3_a1
M. S. Bespalov. Operators of the multiplicative Fourier transform. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2006), pp. 9-23. http://geodesic.mathdoc.fr/item/IVM_2006_3_a1/

[1] Efimov A. V., Karakulin A. F., “O kontinualnom analoge periodicheskikh multiplikativnykh ortonormirovannykh sistem”, DAN SSSR, 218:2 (1974), 268–271 | MR | Zbl

[2] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha. Teoriya i primeneniya, Nauka, M., 1987, 344 pp. | MR | Zbl

[3] Efimov A. V., Zolotareva S. Yu., “Multiplikativnyi integral Fure i ego diskretnye analogi”, Analysis Mathematica, 1979, no. 5, 179–199 | MR | Zbl

[4] Bespalov M. S., Multiplikativnye preobrazovaniya Fure v $L^p$, Dep. v VINITI 08.01.81, No 100-82, Mosk. in-t, M., 1981, 21 pp.

[5] Bespalov M. S., “Perestanovki sistem Uolsha, sokhranyayuschie konstanty Lebega”, Matem. zametki, 68:1 (2000), 36–48 | MR | Zbl

[6] 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, 180 pp.

[7] Khyuitt E., Ross K., Abstraktnyi garmonicheskii analiz, t. 2, Mir, M., 1975, 902 pp.

[8] Vilenkin N. Ya., “K teorii integralov Fure na topologicheskikh gruppakh”, Matem. sb., 30 (1952), 233–244 | MR | Zbl

[9] Paley R., “A remarkable system of orthogonal functions”, Proc. London Math. Soc., 34 (1932), 241–279 | DOI | Zbl

[10] Watari C., “On generalized Walsh-Fourier series”, Tohoku Math. J., 10:3 (1958), 211–241 | DOI | MR | Zbl

[11] Young W.-S., “Mean convergence of generalized Walsh–Fourier series”, Trans. Amer. Math. Soc., 218 (1976), 311–320 | DOI | MR | Zbl

[12] Pospelov A. S., “O sobstvennykh funktsiyakh multiplikativnykh preobrazovanii Fure”, Primenenie funktsionalnogo analiza v teorii priblizhenii, Mezhved. sb. nauch. tr., KGU, Kalinin, 1987, 83–90 | MR

[13] Pospelov A. S., “O sobstvennykh funktsiyakh $p$-adicheskogo i diskretnogo preobrazovaniya Fure”, Matem. modelir., 2:10 (1990), 120–131 | MR | Zbl

[14] Efimov A. V., Pospelov A. S., Umnyashkin S. V., “Nekotorye svoistva multiplikativnykh ortonormirovannykh sistem, ispolzuemye v tsifrovoi obrabotke signalov”, Tr. MIAN im. V. A. Steklova, 219, 1997, 137–182 | MR | Zbl

[15] Pal J., “The eigenfunctions of the Walsh-Fourier transform”, Proc. Int. Conf. Approximation and Functions Spaces (Gdansk, 1979), 1981, 553–557 | MR | Zbl

[16] Riss F., Sekefalvi-Nad B., Lektsii po funktsionalnomu analizu, Mir, M., 1979, 587 pp. | MR

[17] Bespalov M. S., Ob operatorakh multiplikativnykh preobrazovanii Fure, Dep. v VINITI 25.10.83, No 5826-83, Mosk. in-t, M., 1983, 27 pp.