Geodesic
Some Problems in the Theory of Analytic Multifunctions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 432-434.

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In this paper we give a series of open problems in the theory of pseudoconcave sets.
Keywords: pseudoconcave set, set-valued function. 
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Azimbaj S. Sadullaev. Some Problems  in the Theory of Analytic Multifunctions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 4, pp. 432-434. http://geodesic.mathdoc.fr/item/JSFU_2008_1_4_a6/

[1] K. Oka, “Note sur les familles de fonctions analytiques multiformes etc.”, J. Sci. Hiroshima Univ. Ser. A, 4 (1934), 93–98

[2] T. Nishino, “Sur les ensembles pseudo concaves”, J. Math. Kyoto Univ., 1–2 (1962), 225–245 | MR | Zbl

[3] H. Yamaguchi, “Sur une uniformite des surfaces constants d'une function entire de deux variables complexes”, J. Math. Kyoto Univ., 13 (1973), 417–433 | MR | Zbl

[4] Z. Slodkowski, “Analytic set-valued functions and spectra”, Math. Ann., 256 (1981), 363–386 | DOI | MR | Zbl

[5] Z. Slodkowski, “An analytic set-valued selection and its applications to the corona theorem, to polynomial hulls and joint spectra”, Ttans. Amer. Math. Soc., 294:1 (1986), 367–378 | DOI | MR

[6] Z. Slodkowski, “Analytic multifunctions, $q$-plurisubharmonic functions and uniform algebras”, Contemp. Math., 32 (1984), 243–257 | MR

[7] Z. Slodkowski, “An open mapping theorem for analytic multifunctions”, Studia Math., 122:2 (1997), 117–21 | MR

[8] B. Berndtsson, T. J. Ranford, “Analytic multifunction, the $\bar\partial$-equation and a proof of the corona theorem”, Pacific J. Math., 124 (1986), 57–72 | MR | Zbl

[9] H. Alexander, J. Wermer, “Polynomial hulls with convex fibers”, Math. Ann., 271 (1985), 99–109 | DOI | MR | Zbl

[10] H. Alexander, J. Wermer, “On the approximation of singularity sets by analytic varieties. II”, Michigan Math J., 32 (1985), 227–235 | DOI | MR | Zbl

[11] H. Alexander, J. Wermer, “Polynomial hulls with convex fibers”, Math. Ann., 271 (1985), 99–109 | DOI | MR | Zbl

[12] H. Alexander, J. Wermer, “Polynomial hulls of sets with intervals as fibers”, Complex Variables Theory Appl., 11:1 (1989), 11–19 | MR | Zbl

[13] A. Sadullaev, E. M. Chirka, “Extension of function with polar singularity”, Math. Sb., 132(174):3 (1987), 383–390 | MR | Zbl

[14] A. Sadullaev, “Rational approximations and pluripolar sets”, Math. Sb., 119(161):1 (1982), 96–118 | MR | Zbl

[15] A. Sadullaev, “On analytic multifunctions”, Matem. Zametki, 83:5 (2008), 715–721 (Russian) | MR