Remarks on the Obrechkoff inequality
Let u be the logarithmic potential of a probability measure μ in the plane that satisfies u ( z ) = u ( z ¯ ) , u ( z ) ≤ u ( | z | ) , z ∈ ℂ , and m(t) = μ{z ∈ ℂ* : | Arg z| ≤ t}. Then 1 a ∫ 0 a m ( t ) d t ≤ a 2 π , for every a ∈ (0, π). This improves and generalizes a result of Obrechkoff on zero...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2016-02, Vol.144 (2), p.703-707 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let u be the logarithmic potential of a probability measure μ in the plane that satisfies
u
(
z
)
=
u
(
z
¯
)
,
u
(
z
)
≤
u
(
|
z
|
)
,
z
∈
ℂ
,
and m(t) = μ{z ∈ ℂ* : | Arg z| ≤ t}. Then
1
a
∫
0
a
m
(
t
)
d
t
≤
a
2
π
,
for every a ∈ (0, π). This improves and generalizes a result of Obrechkoff on zeros of polynomials with positive coefficients.
2010 Mathematics Subject Classification. Primary 30C15, 31A05.
Key words and phrases. Polynomials, logarithmic potential. |
|---|---|
| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/12738 |