@article{SM_1991_70_2_a1,
author = {G. G. Kazaryan and V. N. Markaryan},
title = {Lower bounds for the~functional dimension of the solution space of hypoelliptic operators},
journal = {Sbornik. Mathematics},
pages = {341--353},
year = {1991},
volume = {70},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1991_70_2_a1/}
}
TY - JOUR AU - G. G. Kazaryan AU - V. N. Markaryan TI - Lower bounds for the functional dimension of the solution space of hypoelliptic operators JO - Sbornik. Mathematics PY - 1991 SP - 341 EP - 353 VL - 70 IS - 2 UR - http://geodesic.mathdoc.fr/item/SM_1991_70_2_a1/ LA - en ID - SM_1991_70_2_a1 ER -
G. G. Kazaryan; V. N. Markaryan. Lower bounds for the functional dimension of the solution space of hypoelliptic operators. Sbornik. Mathematics, Tome 70 (1991) no. 2, pp. 341-353. http://geodesic.mathdoc.fr/item/SM_1991_70_2_a1/
[1] Pontrjagin L., Schnirelman L., “Sur une propiété metrique de la dimension”, Ann. Math., 33 (1921), 156–162 | DOI | MR
[2] Gurevich V., Volmen G., Teoriya razmernosti, IL, M., 1948
[3] Kolmogorov A. N., “Otsenki minimalnogo chisla elementov $\varepsilon$-setei v razlichnykh funktsionalnykh prostranstvakh”, UMN, 10:1 (1955), 192–193
[4] Vitushkin A. G., “K trinadtsatoi probleme Gilberta”, DAN SSSR, 95:4 (1955), 701–704
[5] Kolmogorov A. N., Tikhomirov V. M., “$\varepsilon$-entropiya i $\varepsilon$-emkost mnozhestv v funktsionalnykh prostranstvakh”, UMN, XIV:2(96) (1959), 3–86 | MR
[6] Gelfand I. M., Vilenkin N. Ya., Obobschennye funktsii, vyp. 4, M., 1961
[7] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1967 | MR
[8] Tanaka S., “The $\varepsilon$-entropy of some class of harmonic functions”, Proc. Japan Acad., 39:2 (1936), 85–88 | DOI | MR
[9] Kömura Y., “Die Nuklearität der Lösungsräume der Hypoellptischen Gleichungen”, Funcialay Ekvacioj, 9 (1966), 313–324 | MR
[10] Kolmogorov A. N., “O lineinoi razmernosti topologicheskikh vektornykh prostranstv”, DAN SSSR, 120:2 (1958), 239–242 | MR
[11] Margaryan V. N., Kazaryan G. G., “O funktsionalnoi razmernosti prostranstva reshenii gipoellipticheskikh uravnenii”, Matem. sb., 115(157) (1981), 614–631 | MR | Zbl
[12] Margaryan V. N., “Funktsionalnaya razmernost prostranstv reshenii nekotorykh klassov gipoellipticheskikh uravnenii”, Izv. AN ArmSSR. Matematika, 17:3 (1982), 182–201 | MR
[13] Zielezny Z., “On the functional dimension of the space of solutions of $\mathrm{PDE}$”, J. Diff. Equat., 18:2 (1975), 340–345 | DOI | MR | Zbl
[14] Langenbruch M., “On the functional dimension of solution spaces of Hypoeliiptic partial differential operators”, Math. Ann., 272 (1985), 217–229 | DOI | MR | Zbl
[15] Khërmander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, t. 2, Mir, M., 1986
[16] Langenbruch M., “$P$-Functionale und Raudwerte zu hypoelliptischen Differentialoperatoren”, Math. Ann., 239 (1979), 313–324 | DOI | MR
[17] Mikhailov V. P., “O povedenii na beskonechnosti odnogo klassa mnogochlenov”, Tr. MIAN, 91 (1967), 59–80
[18] Cattabriga L., “Uno spazio funzionale conesso ad una classe di operatori ipoellitici”, Inst. Naz. Alta Mat. Bologna, 7 (1971), 547–558 | MR | Zbl
[19] Kazaryan G. G., “O gipoellipticheskikh polinomakh”, DAN SSSR, 214:5 (1974), 1016–1019 | Zbl