Extremal problems related to the John uniqueness theorem
Algebra i analiz, Tome 21 (2009) no. 5, pp. 37-69.

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

The spectrum structure problem is considered for a distribution that is periodic in the mean and satisfies uniqueness conditions of John type. The solution of this problem is obtained for a wide class of distributions on arbitrary Riemannian two-point-homogeneous spaces.
@article{AA_2009_21_5_a2,
     author = {V. V. Volchkov and Vit. V. Volchkov},
     title = {Extremal problems related to the {John} uniqueness theorem},
     journal = {Algebra i analiz},
     pages = {37--69},
     publisher = {mathdoc},
     volume = {21},
     number = {5},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AA_2009_21_5_a2/}
}
TY  - JOUR
AU  - V. V. Volchkov
AU  - Vit. V. Volchkov
TI  - Extremal problems related to the John uniqueness theorem
JO  - Algebra i analiz
PY  - 2009
SP  - 37
EP  - 69
VL  - 21
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2009_21_5_a2/
LA  - ru
ID  - AA_2009_21_5_a2
ER  - 
%0 Journal Article
%A V. V. Volchkov
%A Vit. V. Volchkov
%T Extremal problems related to the John uniqueness theorem
%J Algebra i analiz
%D 2009
%P 37-69
%V 21
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2009_21_5_a2/
%G ru
%F AA_2009_21_5_a2
V. V. Volchkov; Vit. V. Volchkov. Extremal problems related to the John uniqueness theorem. Algebra i analiz, Tome 21 (2009) no. 5, pp. 37-69. http://geodesic.mathdoc.fr/item/AA_2009_21_5_a2/

[1] John F., “Abhängigkeiten zwischen den Flächenintegralen einer stetigen Funktion”, Math. Ann., 111 (1935), 541–559 | DOI | MR | Zbl

[2] Ion F., Ploskie volny i sfericheskie srednie v primenenii k differentsialnym uravneniyam s chastnymi proizvodnymi, IL, M., 1958

[3] Volchkov V. V., Integral geometry and convolution equations, Kluwer, Dordrecht, 2003 | MR | Zbl

[4] Smith J. D., “Harmonic analysis of scalar and vector fields in $\mathbb R^n$”, Proc. Cambridge Philos. Soc., 72 (1972), 403–416 | DOI | MR | Zbl

[5] Levin B. Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956

[6] Leontev A. F., Posledovatelnosti polinomov iz eksponent, Nauka, M., 1980 | MR

[7] Lyubich Yu. I., “K teoreme edinstvennosti dlya funktsii, periodicheskikh v srednem”, Zap. nauch. semin. LOMI, 81, 1978, 166

[8] Kargaev P. P., “O nulyakh funktsii, periodicheskikh v srednem”, Mat. zametki, 37:3 (1985), 322–325 | MR | Zbl

[9] Kusis P., Vvedenie v teoriyu prostranstv $H^p$ s prilozheniem dokazatelstva Volffa teoremy o korone, Mir, M., 1984 | MR

[10] Quinto E. T., “Pompeiu transforms on geodesic spheres in real analytic manifolds”, Israel J. Math., 84 (1993), 353–363 | DOI | MR | Zbl

[11] Zaraiskii D. A., “Utochnenie teoremy edinstvennosti dlya reshenii uravneniya svërtki”, Tr. IPMM NAN Ukrainy, 12, 2006, 69–75 | MR

[12] Volchkov V. V., “Teoremy edinstvennosti dlya reshenii uravneniya svërtki na simmetricheskikh prostranstvakh”, Izv. RAN. Ser. mat., 70:6 (2006), 3–18 | MR | Zbl

[13] Volchkov V. V., “Lokalnaya teorema o dvukh radiusakh na simmetricheskikh prostranstvakh”, Mat. sb., 198:11 (2007), 21–46 | MR | Zbl

[14] Volchkov Vit. V., “O funktsiyakh s nulevymi sharovymi srednimi na kompaktnykh dvukhtochechno-odnorodnykh prostranstvakh”, Mat. sb., 198:4 (2007), 21–46 | MR | Zbl

[15] Khelgason S., Gruppy i geometricheskii analiz, Mir, M., 1987 | MR

[16] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, T. 1, Mir, M., 1986

[17] Mostow G. D., Strong rigidity of locally symmetric spaces, Ann. of Math. Stud., 78, Princeton Univ. Press, Princeton, NJ, 1973 | MR | Zbl

[18] Helgason S., Geometric analysis on symmetric spaces, Math. Surveys Monogr., 39, Amer. Math. Soc., Providence, RI, 1994 | MR | Zbl

[19] Riekstynsh E. Ya, Asimptoticheskie razlozheniya integralov, T. 1, Zinatne, Riga, 1974

[20] Volchkov V. V., Volchkov Vit. V., Uniqueness theorems and description of solutions for convolution equations on symmetric spaces and for the twisted convolution equations on $\mathbb C^n$, DonNU, Donetsk, 2005

[21] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, T. 2, Nauka, M., 1974

[22] Stein I., Veis G., Vvedenie v garmonicheskii analiz na evklidovykh prostranstvakh, Mir, M., 1974 | Zbl

[23] Edvards P., Ryady Fure v sovremennom izlozhenii, T. 1, Mir, M., 1985