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| Titel: |
Local residues and discrete sets of uniqueness |
| Auteur: |
Vidras, Alekos |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 40 (1999) nr. 1 pagina's 63-92 |
| Jaar: |
1999 |
| Inhoud: |
If [image omitted] then by TГς, we denote the domain of C2 defined by [image omitted] . If B(TГσ denotes the space of bounded holomorphic functions defined in the domain TГς then the following is true. Let [image omitted] be a sequence of points tending to infinity and satisfying [image omitted] . Let also the sequence [image omitted] satisfies [image omitted] for every [image omitted] and for some constant 0 < d < l. Assume that the counting function n{λm}(r) satisfies [image omitted] eventually. If [image omitted] then the sequence {(λn, μn)} is a set of uniqueness for the space B(TГς). That is if g ε B(TГς) and g(λn, μn)=0 for every nε N then g≡0. We prove the above statement by using local residues an of a global meromorphic (2,0) form, whose isolated “poles” are the points (λn, μn) n ε N, in order to express the inverse Laplace Transform σ of an appropriately chosen meromorphic form [image omitted] as a “series” [image omitted] . As a consequence of this result we have the following variation of a Muntz-Szasz theorem in [image omitted] Let [image omitted] be a sequence as in the uniqueness theorem above. Then the linear span of [image omitted] is dense in the space [image omitted] of continuous functions vanishing at infinity if and only if [image omitted] The same theorems can be proven in [image omitted] with suitable modifications. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 3 van 5 gevonden artikelen
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