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Ryuichi Ashino - One of the best experts on this subject based on the ideXlab platform.

Martin Lamprecht - One of the best experts on this subject based on the ideXlab platform.

  • Suffridge’s Convolution Theorem for Polynomials with Zeros in the Unit Disk
    Computational Methods and Function Theory, 2016
    Co-Authors: Martin Lamprecht
    Abstract:

    In 1976, Suffridge proved an intriguing Theorem regarding the Convolution of polynomials with zeros only on the unit circle. His result generalizes a special case of the fundamental Grace–Szego Convolution Theorem, but so far it is an open problem whether there is a Suffridge-like extension of the general Grace–Szego Convolution Theorem. In this paper, we show that Suffridge’s Convolution Theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension for one further special case of the Grace–Szego Convolution Theorem.

  • suffridge s Convolution Theorem for polynomials with zeros in the unit disk
    Computational Methods and Function Theory, 2016
    Co-Authors: Martin Lamprecht
    Abstract:

    In 1976, Suffridge proved an intriguing Theorem regarding the Convolution of polynomials with zeros only on the unit circle. His result generalizes a special case of the fundamental Grace–Szego Convolution Theorem, but so far it is an open problem whether there is a Suffridge-like extension of the general Grace–Szego Convolution Theorem. In this paper, we show that Suffridge’s Convolution Theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension for one further special case of the Grace–Szego Convolution Theorem.

  • suffridge s Convolution Theorem for polynomials with zeros in the unit disk
    arXiv: Complex Variables, 2014
    Co-Authors: Martin Lamprecht
    Abstract:

    In 1976 Suffridge proved an intruiging Theorem regarding the Convolution of polynomials with zeros only on the unit circle. His result generalizes a special case of the fundamental Grace-Szeg\"o Convolution Theorem, but so far it is an open problem whether there is a Suffridge-like extension of the general Grace-Szeg\"o Convolution Theorem. In this paper we try to approach this question from two different directions: First, we show that Suffridge's Convolution Theorem holds for a certain class of polynomials with zeros in the unit disk and thus obtain an extension of one further special case of the Grace-Szeg\"o Convolution Theorem. Second, we present non-circular zero domains which stay invariant under the Grace-Szeg\"o Convolution hoping that this will lead to further analogs of Suffridge's Convolution Theorem.

  • suffridge s Convolution Theorem for polynomials and entire functions having only real zeros
    arXiv: Classical Analysis and ODEs, 2012
    Co-Authors: Martin Lamprecht
    Abstract:

    We present a Suffridge-like extension of the Grace-Szeg\"o Convolution Theorem for polynomials and entire functions with only real zeros. Our results can also be seen as a $q$-extension of P\'olya's and Schur's characterization of multiplier sequences. As a limit case we obtain a new characterization of all log-concave sequences in terms of the zero location of certain associated polynomials. Our results also lead to an extension of Ruscheweyh's Convolution lemma for functions which are analytic in the unit disk and to new necessary conditions for the validity of the Riemann Conjecture.

  • an extension of suffridge s Convolution Theorem
    Journal of Mathematical Analysis and Applications, 2010
    Co-Authors: Martin Lamprecht
    Abstract:

    Abstract We present an extension of Suffridge's Convolution Theorem for polynomials with restricted zeros on the unit circle. We also discuss a possible extension of the Theorem of Laguerre for those polynomials and give an answer to a long-standing open question by Suffridge regarding an extension of the Theorem of Gaus–Lucas.

Andrew Comech - One of the best experts on this subject based on the ideXlab platform.

Mawardi Bahri - One of the best experts on this subject based on the ideXlab platform.

Rafael Robles - One of the best experts on this subject based on the ideXlab platform.

  • the Convolution Theorem for the continuous wavelet tranform
    Signal Processing, 2004
    Co-Authors: Antonio F Perezrendon, Rafael Robles
    Abstract:

    We study the application of the continuous wavelet transform to perform signal filtering processes. We first show that the Convolution and correlation of two wavelet functions satisfy the required admissibility and regularity conditions. By using these new wavelet functions to analyze both Convolutions and correlations, respectively, we derive Convolution and correlation Theorems for the continuous wavelet transform and show them to be similar to that of other joint spatial/spatial-frequency or time/frequency representations. We then investigate the effect of multiplying the continuous wavelet transform of a given signal by a related transfer function and show how to perform spatially variant filtering operations in the wavelet domain. Finally, we present numerical examples showing the usefulness of applying the Convolution Theorem for the continuous wavelet transform to perform signal restoration in the presence of additive noise.