Khabibullin, B. N.; Khabibullin, F. B.; Cherednikova, L. Yu. Subsequences of zeros for classes of holomorphic functions, their stability, and the entropy of arcwise connectedness. II. (English. Russian original) Zbl 1206.30075 St. Petersbg. Math. J. 20, No. 1, 131-162 (2009); translation from Algebra Anal. 20, No. 1, 190-236 (2008). Summary: Let \( \Omega\) be a domain in the complex plane \( \mathbb{C}, H(\Omega)\) the space of functions holomorphic in \( \Omega\), and \( \mathcal P\) a family of functions subharmonic in \( \Omega\). Denote by \( H_{\mathcal P}(\Omega )\) the class of functions \( f\in H(\Omega)\) satisfying \( | f(z)|\leq C_f\exp p_f(z)\) for all \( z\in \Omega\), where \( p_f \in \mathcal P\) and \( C_f\) is a constant. Conditions are found ensuring that a sequence \( \Lambda =\{\lambda_k\} \subset \Omega\) be a subsequence of zeros for various classes \( H_{\mathcal P}(\Omega )\). As a rule, the results and the method are new already when \( \Omega=\mathbb{D}\) is the unit circle and \( \mathcal P\) is a system of radial majorants \( p(z)=p(| z|)\). For part I, cf. ibid. 20, No. 1, 101–129 (2009); translation from Algebra Anal. 20, No. 1, 146–189 (2008). Cited in 2 Documents MSC: 30H05 Spaces of bounded analytic functions of one complex variable Keywords:holomorphic function; algebra of functions; weighted space; nonuniqueness sequence × Cite Format Result Cite Review PDF Full Text: DOI References: [1] B. N. Khabibullin, F. B. Khabibullin, and L. Yu. Cherednikova, Subsequences of zeros for classes of holomorphic functions, their stability, and the entropy of arcwise connectedness. I, Algebra i Analiz 20 (2008), no. 1, 146 – 189 (Russian, with Russian summary); English transl., St. Petersburg Math. J. 20 (2009), no. 1, 101 – 129. · Zbl 1206.30074 [2] V. S. Azarin, Asymptotic behavior of subharmonic functions of finite order, Mat. Sb. (N.S.) 108(150) (1979), no. 2, 147 – 167, 303 (Russian). [3] Kurt Leichtweiss, Konvexe Mengen, Springer-Verlag, Berlin-New York, 1980 (German). Hochschultext. · Zbl 0374.52002 [4] Thomas Ransford, Potential theory in the complex plane, London Mathematical Society Student Texts, vol. 28, Cambridge University Press, Cambridge, 1995. · Zbl 0828.31001 [5] Boris Korenblum, An extension of the Nevanlinna theory, Acta Math. 135 (1975), no. 3-4, 187 – 219. · Zbl 0323.30030 · doi:10.1007/BF02392019 [6] Kristian Seip, On a theorem of Korenblum, Ark. Mat. 32 (1994), no. 1, 237 – 243. · Zbl 0812.30003 · doi:10.1007/BF02559530 [7] Kristian Seip, On Korenblum’s density condition for the zero sequences of \?^{-\?}, J. Anal. Math. 67 (1995), 307 – 322. · Zbl 0845.30014 · doi:10.1007/BF02787795 [8] Joaquim Bruna and Xavier Massaneda, Zero sets of holomorphic functions in the unit ball with slow growth, J. Anal. Math. 66 (1995), 217 – 252. · Zbl 0858.32009 · doi:10.1007/BF02788823 [9] Daniel H. Luecking, Zero sequences for Bergman spaces, Complex Variables Theory Appl. 30 (1996), no. 4, 345 – 362. · Zbl 0871.30004 [10] Haakan Hedenmalm, Boris Korenblum, and Kehe Zhu, Theory of Bergman spaces, Graduate Texts in Mathematics, vol. 199, Springer-Verlag, New York, 2000. · Zbl 0955.32003 [11] B. N. Khabibullin, Zero (sub)sets for spaces of holomorphic functions and (sub)harmonic minorants, Electronic Archive at LANL, 18 Dec 2004, 42 pp., http://arxiv.org/abs/math.CV/0412359. [12] F. A. Šamojan, A factorization theorem of M. M. Džrbašjan and the characteristic of zeros of functions analytic in the circle with a majorant of finite growth, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 13 (1978), no. 5-6, 405 – 422, 541 (Russian, with English and Armenian summaries). [13] W. K. Hayman and P. B. Kennedy, Subharmonic functions. Vol. I, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York, 1976. London Mathematical Society Monographs, No. 9. · Zbl 0419.31001 [14] Eliyahu Beller, Factorization for non-Nevanlinna classes of analytic functions, Israel J. Math. 27 (1977), no. 3 – 4, 320 – 330. · Zbl 0361.30012 · doi:10.1007/BF02756490 [15] L. Yu. Cherednikova, Nonuniqueness sequences for weighted algebras of holomorphic functions in the unit disk, Mat. Zametki 77 (2005), no. 5, 775 – 787 (Russian, with Russian summary); English transl., Math. Notes 77 (2005), no. 5-6, 715 – 725. · Zbl 1076.30053 · doi:10.1007/s11006-005-0072-5 [16] F. A. Shamoyan, Zeros of functions analytic in the disk and growing near the boundary, Izv. Akad. Nauk Armyan. SSR Ser. Mat. 18 (1983), no. 1, 15 – 27 (Russian, with English and Armenian summaries). [17] B. N. Khabibullin, Growth of entire functions with prescribed zeros and representation of meromorphic functions, Mat. Zametki 73 (2003), no. 1, 120 – 134 (Russian, with Russian summary); English transl., Math. Notes 73 (2003), no. 1-2, 110 – 124. · Zbl 1025.30025 · doi:10.1023/A:1022182219464 [18] B. N. Khabibullin, Zero subsets, representation of meromorphic functions, and Nevanlinna characteristics in a disk, Mat. Sb. 197 (2006), no. 2, 117 – 136 (Russian, with Russian summary); English transl., Sb. Math. 197 (2006), no. 1-2, 259 – 279. · Zbl 1143.30017 · doi:10.1070/SM2006v197n02ABEH003757 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.