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Value Distribution Theory and Related Topics pp 131–166Cite as

Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences

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Part of the book series: Advances in Complex Analysis and Its Applications ((ACAA,volume 3))

Abstract

An important chapter in the theory of distribution of zeros of polynomials and transcendental entire functions pertains to the study of linear operators acting on entire functions. This article surveys some recent developments (as well as some classical results) involving some specific classes of linear operators called multiplier sequences and complex zero decreasing sequences. This expository article consists of four parts: Open problems and background information, Composition theorems (Section 2), Multiplier sequences and the Laguerre-Pólya class (Section 3) and Complex zero decreasing sequences (Section 4). A number of open problems and questions are also included.

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Authors and Affiliations

  1. Department of Mathematics, University of Hawaii, Honolulu, HI, 96822

    Thomas Craven & George Csordas

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  1. Thomas Craven
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  2. George Csordas
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Editors and Affiliations

  1. National Academy of Sciences of Armenia, Yerevan, Armenia

    G. Barsegian

  2. University of Joensuu, Joensuu, Finland

    I. Laine

  3. Hong Kong University of Science and Technology, Hong Kong, China

    C. C. Yang

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Craven, T., Csordas, G. (2004). Composition Theorems, Multiplier Sequences and Complex Zero Decreasing Sequences. In: Barsegian, G., Laine, I., Yang, C.C. (eds) Value Distribution Theory and Related Topics. Advances in Complex Analysis and Its Applications, vol 3. Springer, Boston, MA. https://doi.org/10.1007/1-4020-7951-6_6

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