Dual representation of superlinear functionals and its applications in function theory. II. (English. Russian original) Zbl 1052.32004

Khabibullin, B. N.

Izv. Math. 65, No. 5, 1017-1039 (2001); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 65, No. 5, 167-190 (2001).

Summary: The results of the first part of this work [see the author, Izv. Math. 65, No. 4, 835–852 (2001; Zbl 1030.46003)] are used only in §7 of this paper, from which subsequent results follow. We pose new dual problems for weight spaces of holomorphic functions of one and several variables defined on a domain in \(\mathbb{C}^n\), namely, the problem of non-triviality of a given space, description of zero sets, description of sets of (non-)uniqueness, existence of holomorphic functions of certain classes that “suppress” the growth of a given holomorphic function, and representation of meromorphic functions as quotients of holomorphic functions contained in a given space.

MSC:

32A10	Holomorphic functions of several complex variables
32A20	Meromorphic functions of several complex variables
32A27	Residues for several complex variables
32A60	Zero sets of holomorphic functions of several complex variables

Keywords:

weight spaces of holomorphic functions; non-triviality; zero sets; sets of (non-)uniqueness; existence; growth; meromorphic functions

Citations:

Zbl 1030.46003