On Bernstein's Inequality
1979 ◽
Vol 31
(2)
◽
pp. 347-353
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Keyword(s):
1. Introduction and statement of results. If pn(z) is a polynomial of degree at most n, then according to a famous result known as Bernstein's inequality (for references see [4])(1)Here equality holds if and only if pn(z) has all its zeros at the origin and so it is natural to seek for improvements under appropriate assumptions on the zeros of pn(z). Thus, for example, it was conjectured by P. Erdös and later proved by Lax [2] that if pn(z) does not vanish in │z│ < 1, then (1) can be replaced by(2)On the other hand, Turán [5] showed that if pn(z) is a polynomial of degree n having all its zeros in │z│ ≦ 1, then(3)
1924 ◽
Vol 22
(3)
◽
pp. 282-286
Keyword(s):
1985 ◽
Vol 101
(1-2)
◽
pp. 99-110
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1968 ◽
Vol 11
(4)
◽
pp. 527-531
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Keyword(s):
1978 ◽
Vol 36
(1)
◽
pp. 216-217
Keyword(s):
1968 ◽
Vol 64
(1)
◽
pp. 1-1
◽