A variant of Carathéodory's problem
1968 ◽
Vol 16
(1)
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pp. 43-48
In this note we ask two questions and answer one. The questions can be combined as follows:Does there exist a polynomial of the formwhich starts with prescribed complex coefficients c0, …, cr–1; and satisfiesThese differ from the classical problems of Carathéodory in one essential respect: the values of p and its first r–1 derivatives are given at the point z = 1 on the circumference of the unit circle, while in the original problem they were given at z = 0. Carathéodory's own answer was in terms of his “moment curve”, but the forms studied a few years later by Toeplitz yield a more convenient statement of the solution.
1962 ◽
Vol 58
(2)
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pp. 229-234
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1956 ◽
Vol 52
(1)
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pp. 49-60
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1962 ◽
Vol 14
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pp. 540-551
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Keyword(s):
1994 ◽
Vol 37
(1)
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pp. 73-89
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Keyword(s):
1964 ◽
Vol 16
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pp. 721-728
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1970 ◽
Vol 17
(1)
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pp. 23-36
Keyword(s):
1953 ◽
Vol 49
(2)
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pp. 190-193
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Keyword(s):
1962 ◽
Vol 13
(2)
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pp. 173-174
1978 ◽
Vol 21
(1)
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pp. 17-23
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Keyword(s):
1949 ◽
Vol 45
(2)
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pp. 207-212
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