By Carlos A. Berenstein (auth.), William E. Kirwan, Lawrence Zalcman (eds.)

ISBN-10: 3540075488

ISBN-13: 9783540075486

ISBN-10: 3540380884

ISBN-13: 9783540380887

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Extra info for Advances in Complex Function Theory: Proceedings of Seminars Held at Maryland University, 1973/74

Example text

And the result the left of [8]. THEOREM If 4. the lower order If r n sin and lower ' 1 is p r e c i s e l y inequality Heins the ~ k is e v e n he, where u = examples now when extend if pDints u k 8 is sharp. u : r 89 is odd, since is h a r m o n i c (gig) = x + iy, For by 8 + 2~. except is e v i d e n t l y tracts, where k > i, v : I m ( x + iy) n = polynomials 8 + i sin e) k. k 1 ~ ~ ~ k. h. However, Heins' theorem lies m u c h deeper than the corresponding 32 result for harmonic polynomials.

If function 2. entire only and from Let v--+0 inside functions D function8 D. v(z) as has is linear 9 a domain approaches It is n a t u r a l can have be a plane 3 cases the domain f = u + iv the f o l l o w i n g z v such same and any to ask tract. let that F(D) v has as a tract D finite boundary in w h a t w a y A full two answer be the class D is of as a tract. are p o s si b l e tThe results of this section represent Joint work with Brannan, Fuchs and Kuran. Full proofs will be published in [3].

Sb. 68 (1965), 549-560 (in Russian). On a univalence criterion for regular functions and the dispersion of their coefficients, Mat. Sb. 74 (1967), 133-146 3. (in Russian). L. Duren, Estimation of coefficients of univalent functions by a Tauberian remainder theorem, J. London Math. Soc. 8 (1974), 279-282. 4. K. Hayman, The asymptotic behaviour of p-valent functions, Proc. London Math. Soe. 5 (1955), 257-284. 5. K. Hayman, Multivalent 1958. 6. J. Korevaar, Another numerical Tauberian theorem for power series, Nederl.

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Advances in Complex Function Theory: Proceedings of Seminars Held at Maryland University, 1973/74 by Carlos A. Berenstein (auth.), William E. Kirwan, Lawrence Zalcman (eds.)


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