Zeros of successive derivatives and iterated operators on analytic functions
HTML articles powered by AMS MathViewer
- by J. K. Shaw and C. L. Prather PDF
- Proc. Amer. Math. Soc. 79 (1980), 225-232 Request permission
Abstract:
For a function f analytic in the closed disc $|z| \leqslant 1$, we study the behavior of zeros of the successive iterates $({\theta ^n}f)(z),n = 0,1,2, \ldots$, where $\theta = {(z + \alpha )^{p + 1}}d/dz$. We find that such behavior closely parallels that for the ordinary derivative operator. Using change-of-variable methods, we obtain information on zeros of derivatives of functions analytic in half-planes.References
- R. P. Boas, Zeros of successive derivatives of a function analytic at infinity, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. 602-633 (1978), 51–52 (1979). MR 580421
- J. D. Buckholtz, Successive derivatives of analytic functions, Indian J. Math. 13 (1971), 83–88. MR 333176
- J. D. Buckholtz and J. L. Frank, Whittaker constants, Proc. London Math. Soc. (3) 23 (1971), 348–370. MR 296297, DOI 10.1112/plms/s3-23.2.348
- J. D. Buckholtz and J. L. Frank, Whittaker constants. II, J. Approximation Theory 10 (1974), 112–122. MR 349997, DOI 10.1016/0021-9045(74)90110-5
- J. L. Frank and J. K. Shaw, Abel-Gončarov polynomial expansions, J. Approximation Theory 10 (1974), 6–22. MR 346161, DOI 10.1016/0021-9045(74)90092-6
- Einar Hille, Analytic function theory. Vol. II, Introductions to Higher Mathematics, Ginn and Company, Boston, Mass.-New York-Toronto, Ont., 1962. MR 0201608
- D. V. Widder, The inversion of the Laplace integral and the related moment problem, Trans. Amer. Math. Soc. 36 (1934), no. 1, 107–200. MR 1501737, DOI 10.1090/S0002-9947-1934-1501737-7
Additional Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 79 (1980), 225-232
- MSC: Primary 30C15
- DOI: https://doi.org/10.1090/S0002-9939-1980-0565344-9
- MathSciNet review: 565344