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Decrease of bounded holomorphic functions along discrete sets
| Content Provider | Semantic Scholar |
|---|---|
| Author | Thomas, J. J. March |
| Copyright Year | 2001 |
| Abstract | We provide results of uniqueness for holomorphic functions in the Nevanlinna class bridging those previously obtained by Hayman and Lyubarskii-Seip. Namely, we propose certain classes of hyperbolically separated sequences in the disk, in terms of the rate of non-tangential accumulation to the boundary (the endpoints of this spectrum of classes being respectively the sequences with a non-tangential cluster set of positive measure, and the sequences violating the Blaschke condition); and for each of those classes, we give a critical condition of radial decrease on the modulus which will force a Nevanlinna class function to vanish identically. 1 Definitions and results Let D be the unit disk in the complex plane. We are interested in the allowable decrease of the modulus of a nontrivial bounded holomorphic function f ∈ H(D) along a discrete sequence {ak} ⊂ D. Notice that those problems are actually the same if we replace H by the Nevanlinna class N , since on the one hand H ⊂ N and on the other hand, for any f ∈ N , we can write f = f1/f2 where |f2(z)| ≤ 1 for all z ∈ D, thus |f1(z)| ≤ |f(z)|, and f1 ∈ H . This also means in particular that any Hardy space H could be substituted for H. On the other hand it seems clear that the situation in Bergman spaces has to be quite different, see [Bo] for related results. When {ak} satisfies the Blaschke condition ∞ |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0106048v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0106048v1.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Ak-Tracin Bridging (networking) Bronchiolitis Obliterans Call of Duty: Black Ops Class Courant–Friedrichs–Lewy condition Modulus of continuity Nevanlinna Prize Radial (radio) Reputation management Tree accumulation |
| Content Type | Text |
| Resource Type | Article |
