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| Titel: |
On the zeros of solutions of an extremal problem in H1 |
| Auteur: |
Inoue, Jyunji Nakazi, Takahiko |
| Verschenen in: |
Complex variables and elliptic equations |
| Paginering: | Jaargang 40 (2000) nr. 3 pagina's 173-188 |
| Jaar: |
2000 |
| Inhoud: |
For a nonzero function f in H1, the classical Hardy space on the unit disc, we put [image omitted] .. The intersection of Sf and the unit sphere in H1 is a solution set of a certain extremal problem in H1. It is known that Sf can be represented in the form Sf= SB × g0, where B is a Blaschke product and g0 is a function in H1 with Sg0 = {λ g0: λ > 0}. Also it is known that the linear span of Sf is finite dimensional if and only if B is a finite Blaschke product, and when B is a finite Blaschke product, we can describe completely the set SB and the zeros of functions in SB. In this paper we study the set of zeros of functions in SB when B is an infinite Blaschke product whose set of singularities is not the whole circle. In particular, we study the behavior of zeros of functions in SB in the sectors of the form: δ= {reiθ:0 < r ≤ 1c1 < θ < c2} on which the zeros of B has no accumulation points, and establish a convergence order theorem for the zeros in δ of functions in SB. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 7 van 8 gevonden artikelen
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