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Approximation of analytic functions by rational functions with prescribed poles

✍ Scribed by Gaetano Fichera

Publisher
John Wiley and Sons
Year
1970
Tongue
English
Weight
473 KB
Volume
23
Category
Article
ISSN
0010-3640

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✦ Synopsis

From (1) it follows that y ( z ) has in zk a zero of order not less than vk .

Since y ( z ) is holomorphic in the neighborhood of every point of %'K (including z = a), it follows from Hypothesis 6, that y ( z ) vanishes identically in VK. On the other hand, we have for large IzJ of 5.

1 We say that zo (which may be the point 03 of the complex plane) is a compuctnesspoinf for the sequence { z k } if, for an arbitrary neighborhood I of zo , there exist infinitely many values of the index k auch that z k E I.

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