Stieltjes Functions and Hurwitz Stable Entire Functions |
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Authors: | Victor Katsnelson |
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Institution: | 1. Department of Mathematics, The Weizmann Institute, Rehovot, 76100, Israel
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Abstract: | The concept of stability, originally introduced for polynomials, will be extended to apply to the class of entire functions.
This generalization will be called Hurwitz stablility and the class of Hurwitz stable functions will serve as the main focus
of this paper. A first theorem will show how, given a function of either of the Stieltjes classes, a Hurwitz stable function
might be constructed. A second approach to constructing Hurwitz stable functions, based on using additional functions from
the Laguerre-Pólya class, will be presented in a second theorem. |
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Keywords: | |
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