Assume that f is an entire function and satisfies the estimate |f(z)| C(1+z) for all...
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Assume that f is an entire function and satisfies the estimate |f(z)| ≤ C(1+z)" for all z = C, for some positive integer n. Conclude that f is a polynomial in z of degree <n. Hint: Apply Cauchy Inequalities in the disk D(0, R), and let R→ ∞ to show that f(n+¹)(x) = 0 for all z € C. Assume that f is an entire function and satisfies the estimate |f(z)| ≤ C(1+z)" for all z = C, for some positive integer n. Conclude that f is a polynomial in z of degree <n. Hint: Apply Cauchy Inequalities in the disk D(0, R), and let R→ ∞ to show that f(n+¹)(x) = 0 for all z € C.
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Related Book For
Elementary Linear Algebra with Applications
ISBN: 978-0132296540
9th edition
Authors: Bernard Kolman, David Hill
Posted Date:
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