Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2003_15_1_a0, author = {S. Ya. Khavinson}, title = {Duality relations in the theory of analytic capacity}, journal = {Algebra i analiz}, pages = {3--62}, publisher = {mathdoc}, volume = {15}, number = {1}, year = {2003}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2003_15_1_a0/} }
S. Ya. Khavinson. Duality relations in the theory of analytic capacity. Algebra i analiz, Tome 15 (2003) no. 1, pp. 3-62. http://geodesic.mathdoc.fr/item/AA_2003_15_1_a0/
[1] Ahlfors L., “Bounded analytic functions”, Duke Math. J., 14:1 (1947), 1–11 | DOI | MR | Zbl
[2] Garnett J., Analytic capacity and measure, Lecture Notes in Math., 297, Springer-Verlag,, Berlin–New York, 1972 | MR | Zbl
[3] Garnett Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl
[4] Gamelin T., Ravnomernye algebry, Mir, M., 1973 | Zbl
[5] Vitushkin A. G., “Analiticheskaya emkost mnozhestv v zadachakh teorii priblizhenii”, Uspekhi mat. nauk, 22:6(138) (1967), 141–199 | MR
[6] Vitushkin A. G., “Ravnomernye priblizheniya golomorfnymi funktsiyami”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 4, VINITI, M., 1975, 5–12 | MR
[7] Khavinson S. Ya., Dopolnitelnye voprosy teorii ustranimykh osobennostei analiticheskikh funktsii, MISI, M., 1982
[8] Khavinson S. Ya., “Summy Golubeva: teoriya ekstremalnykh zadach tipa zadachi ob analiticheskoi emkosti i soputstvuyuschikh approksimatsionnykh protsessov”, Uspekhi mat. nauk, 54:4(328) (1999), 75–142 | MR | Zbl
[9] Zalcman L., Analytic capacity and rational approximation, Lecture Notes in Math., 50, Springer-Verlag, Berlin–New York, 1968 | MR
[10] Gonchar A. A., Mergelyan S. N., “Teoriya priblizhenii funktsii kompleksnogo peremennogo”, Istoriya otechestvennoi matematiki, T. 4. Kn. 1, Nauk. dumka, Kiev, 1970, 112–193
[11] Melnikov M. S., Sinanyan S. O., “Voprosy teorii priblizhenii funktsii odnogo kompleksnogo peremennogo”, Itogi nauki i tekhn. Ser. Sovrem. probl. mat., 4, VINITI, M., 1975, 143–250
[12] Khavinson S. Ya., “O predstavlenii i priblizhenii funktsii na redkikh mnozhestvakh”, Sovremennye problemy teorii analiticheskikh funktsii, Nauka, M., 1966, 314–318
[13] Melnikov M. S., “Analiticheskaya emkost: diskretnyi podkhod i krivizna mery”, Mat. sb., 186:6 (1995), 57–76 | MR
[14] Calderón A. P., “Cauchy integrals on Lipschitz curves and related operators”, Proc. Nat. Acad. Sci. USA, 74 (1977), 1324–1327 | DOI | MR | Zbl
[15] David G., “Analytic capacity”, Calderón-Zygmund operators, and rectifiability, Publ. Mat., 43, 1999, 3–25 | MR | Zbl
[16] Tolsa X., Curvature of measures, Cauchy singular integral and analytic capacity, Thesis, Univ. Autonoma Barcelona, Barcelona, 1998 | Zbl
[17] Tolsa X., The semiadditivity of analytic capacity, Preprint, 2001, 1–39
[18] Garabedian P. R., “Schwarz's lemma and the Szegő kernel function”, Trans. Amer. Math. Soc., 67 (1949), 1–35 | DOI | MR | Zbl
[19] Garabedian P. R., “The classes $L_p$ and confonnal mapping”, Trans. Amer. Math. Soc., 69 (1950), 392–415 | DOI | MR | Zbl
[20] Khavinson S. Ya., “Ob analiticheskoi emkosti ploskikh mnozhestv, o nekotorykh klassakh analiticheskikh funktsii i ob ekstremalnoi funktsii v lemme Shvartsa dlya proizvolnykh oblastei”, Dokl. AN SSSR, 128:5 (1959), 896–898 | Zbl
[21] Khavinson S. Ya., “Analiticheskaya emkost mnozhestv i raspredeleniya mass”, Dokl. AN SSSR, 128:6 (1959), 1129–1131 | Zbl
[22] Khavinson S. Ya., “Ob analiticheskoi emkosti mnozhestv, sovmestnoi netrivialnosti razlichnykh klassov analiticheskikh funktsii i lemme Shvartsa v proizvolnykh oblastyakh”, Mat. sb., 54(96):1 (1961), 3–50 | MR
[23] Khavinson S. Ya., “Ob approksimatsii na mnozhestvakh analiticheskoi emkosti nul”, Dokl. AN SSSR, 131:1 (1960), 44–46 | Zbl
[24] Khavin V. P., “O prostranstve ogranichennykh regulyarnykh funktsii”, Dokl. AN SSSR, 131:1 (1960), 40–43
[25] Khavin V. P., “O prostranstve ogranichennykh regulyarnykh funktsii”, Sib. mat. zh., 2:4 (1961), 622–638
[26] Valskii R. E., “Neskolko zamechanii ob ogranichennykh funktsiyakh, predstavimykh integralom tipa Koshi–Stiltesa”, Sib. mat. zh., 7:2 (1966), 252–260 | MR
[27] Murai T., “Analytic capacity and the Szegő kernel function”, Linear and Complex Analysis, Problem Book 3. Pt. 2, Lecture Notes in Math., 1574, Springer-Verlag, Berlin, 1994, 158–160 | MR
[28] Murai T., “Construction of $H^1$ functions concerning the estimate of analytic capacity”, Bull. London Math. Soc., 19 (1987), 154–160 | DOI | MR | Zbl
[29] Suita N., “On a metric induced by analytic capacity”, Kōdai Math. Sem. Rep., 25 (1973), 215–218 | DOI | MR | Zbl
[30] Khavinson S. Ya., “Ob approksimatsii s uchetom velichin koeffitsientov approksimiruyuschikh agregatov”, Tr. Mat. in-ta AN SSSR, 60, 1961, 304–324
[31] Davis Ph., Fan K., “Complete sequences and approximations in normed linear spaces”, Duke Math. J., 24:2 (1957), 183–192 | DOI | MR | Zbl
[32] Khavinson S. Ya., “Nekotorye voprosy polnoty sistem”, Dokl. AN SSSR, 137:4 (1961), 793–796 | Zbl
[33] Khavinson S. Ya., “Nekotorye teoremy o priblizhenii s uchetom velichin koeffitsientov approksimiruyuschikh funktsii”, Dokl. AN SSSR, 196:6 (1971), 1283–1286 | Zbl
[34] Khavinson S. Ya., “O ponyatii polnoty, uchityvayuschem velichiny koeffitsientov approksimiruyuschikh polinomov”, Izv. AN ArmSSR. Mat., 6:2–3 (1971), 221–234 | Zbl
[35] Khavinson S. Ya., “O polnykh sistemakh v banakhovykh prostranstvakh”, Izv. AN ArmSSR. Mat., 20:2 (1985), 89–111 | MR | Zbl
[36] Krein M. G., “$L$-problema v abstraktnom lineinom normirovannom prostranstve”, O nekotorykh voprosakh teorii momentov, eds. Akhiezer N. I., Krein M. G., GONTI USSR, Kharkov, 1938, 171–200
[37] Nikolskii S. M., “Priblizhenie funktsii trigonometricheskimi polinomami v srednem”, Izv. AN SSSR. Ser. mat., 10:3 (1946), 207–256
[38] Garkavi A. L., “Teoremy dvoistvennosti dlya priblizhenii posredstvom elementov vypuklykh mnozhestv”, Uspekhi mat. nauk, 16:4 (1961), 141–145 | MR | Zbl
[39] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, MGU, M., 1976 | MR
[40] Korneichuk N. P., Ekstremalnye zadachi teorii priblizheniya, Nauka, M., 1976 | MR
[41] Loran P.-Zh., Approksimatsiya i optimizatsiya, Mir, M., 1975
[42] Golshtein E. G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, Nauka, M., 1971 | MR
[43] Khavinson S. Ya., Chatskaya E. Sh., Sootnosheniya dvoistvennosti i kriterii elementov nailuchshego priblizheniya, MISI, M., 1976
[44] Dei M. M., Normirovannye lineinye prostranstva, IL, M., 1961
[45] Danford N., Shvarts Dzh. T., Lineinye operatory. Obschaya teoriya, IL, M., 1962
[46] Khavinson S. Ya., Faktorizatsiya analiticheskikh funktsii v konechnosvyaznykh oblastyakh, MISI, M., 1981
[47] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M., 1950
[48] Khalmosh P., Teoriya mery, IL, M., 1953
[49] Saks S., Teoriya integrala, IL, M., 1949
[50] Samokhin M. V., “K voprosu o predstavimosti funktsii Alforsa v vide potentsiala Koshi”, Nauch. vestn. Mosk. tekhn. un-ta grazhdanskoi aviatsii, M., 1999, 55–59
[51] Samokhin M. V., “Ob integralnoi formule Koshi v oblastyakh proizvolnoi svyaznosti”, Mat. sb., 191:8 (2000), 113–130 | MR | Zbl
[52] Karleson L., Izbrannye problemy teorii isklyuchitelnykh mnozhestv, Mir, M., 1971 | MR | Zbl
[53] Samokhin M. V., “Ekstremalnye zadachi dlya ogranichennykh analiticheskikh funktsii i klassov $E_p$ v proizvolnykh oblastyakh”, Sb. tr. MISI, 153, 1977, 35–48
[54] David G., “Unrectiflable 1-sets have vanishing analytic capacity”, Rev. Mat. Iberoamericana, 14:2 (1998), 369–479 | MR | Zbl
[55] Nazarov F., Treil S., Volberg A., $T(b)$-theorem and analytical capacity, Preprint, 1998 | MR
[56] Rubel L. A., Shields A. L., “The space of bounded analytic functions on a region”, Ann. Inst. Fourier (Grenoble), 16:1 (1966), 235–277 | MR | Zbl
[57] Aleksandrov P. S., Vvedenie v obschuyu teoriyu mnozhestv i funktsii, GITTL, M.-L., 1948
[58] Naimark M. A., Normirovannye koltsa, Gostekhizdat, M., 1956