The Experts below are selected from a list of 282 Experts worldwide ranked by ideXlab platform
Ryuichi Ashino - One of the best experts on this subject based on the ideXlab platform.
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a Convolution Theorem related to quaternion linear canonical transform
Abstract and Applied Analysis, 2019Co-Authors: Mawardi Bahri, Ryuichi AshinoAbstract:We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion Convolution in the QLCT domain we derive the Convolution Theorem associated with the QLCT and obtain a few consequences.
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logarithmic uncertainty principle Convolution Theorem related to continuous fractional wavelet transform and its properties on a generalized sobolev space
International Journal of Wavelets Multiresolution and Information Processing, 2017Co-Authors: Mawardi Bahri, Ryuichi AshinoAbstract:The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the Convolution Theorem related to the CFrWT is established using the Convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.
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Correlation formulation using relationship between Convolution and correlation in linear canonical transform domain
2017 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR), 2017Co-Authors: Mawardi Bahri, Amir Kamal Amir, Ryuichi AshinoAbstract:The Convolution Theorem for the linear canonical transformation is introduced. Correlation Theorems related to the linear canonical transformation are established by using the relation between Convolution and correlation definitions in the linear canonical transform domains.
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Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform
2012 International Conference on Wavelet Analysis and Pattern Recognition, 2012Co-Authors: Mawardi Bahri, Ryuichi Ashino, Rémi VaillancourtAbstract:A two-dimensional quaternion Fourier transform (QFT) defined with the kernel e - i+j+k/√3 ω · x is proposed. Some fundamental properties, such as Convolution Theorem and Plancherel Theorem are established. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.
Martin Lamprecht - One of the best experts on this subject based on the ideXlab platform.
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Suffridge’s Convolution Theorem for Polynomials with Zeros in the Unit Disk
Computational Methods and Function Theory, 2016Co-Authors: Martin LamprechtAbstract: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.
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suffridge s Convolution Theorem for polynomials with zeros in the unit disk
Computational Methods and Function Theory, 2016Co-Authors: Martin LamprechtAbstract: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.
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suffridge s Convolution Theorem for polynomials with zeros in the unit disk
arXiv: Complex Variables, 2014Co-Authors: Martin LamprechtAbstract: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.
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suffridge s Convolution Theorem for polynomials and entire functions having only real zeros
arXiv: Classical Analysis and ODEs, 2012Co-Authors: Martin LamprechtAbstract: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.
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an extension of suffridge s Convolution Theorem
Journal of Mathematical Analysis and Applications, 2010Co-Authors: Martin LamprechtAbstract: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.
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solutions with compact time spectrum to nonlinear klein gordon and schrodinger equations and the titchmarsh Theorem for partial Convolution
Arnold Mathematical Journal, 2019Co-Authors: Andrew ComechAbstract:We prove that finite energy solutions to the nonlinear Schrodinger equation and nonlinear Klein–Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh Convolution Theorem to partial Convolutions.
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Solutions with Compact Time Spectrum to Nonlinear Klein–Gordon and Schrödinger Equations and the Titchmarsh Theorem for Partial Convolution
Arnold Mathematical Journal, 2019Co-Authors: Andrew ComechAbstract:We prove that finite energy solutions to the nonlinear Schrödinger equation and nonlinear Klein–Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh Convolution Theorem to partial Convolutions.
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solutions with compact time spectrum to nonlinear klein gordon and schroedinger equations and the titchmarsh Theorem for partial Convolution
arXiv: Analysis of PDEs, 2018Co-Authors: Andrew ComechAbstract:We prove that finite energy solutions to the nonlinear Schroedinger equation and nonlinear Klein--Gordon equation which have the compact time spectrum have to be one-frequency solitary waves. The argument is based on the generalization of the Titchmarsh Convolution Theorem to partial Convolutions.
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on the titchmarsh Convolution Theorem for distributions on the circle
arXiv: Functional Analysis, 2011Co-Authors: Andrew Comech, Andrew KomechAbstract:We prove a version of the Titchmarsh Convolution Theorem for distributions on the circle. We show that the "naive form" of the Titchmarsh Theorem could be violated, but that such a violation is only possible for the Convolution of distributions which both possess certain symmetry properties.
Mawardi Bahri - One of the best experts on this subject based on the ideXlab platform.
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a Convolution Theorem related to quaternion linear canonical transform
Abstract and Applied Analysis, 2019Co-Authors: Mawardi Bahri, Ryuichi AshinoAbstract:We introduce the two-dimensional quaternion linear canonical transform (QLCT), which is a generalization of the classical linear canonical transform (LCT) in quaternion algebra setting. Based on the definition of quaternion Convolution in the QLCT domain we derive the Convolution Theorem associated with the QLCT and obtain a few consequences.
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logarithmic uncertainty principle Convolution Theorem related to continuous fractional wavelet transform and its properties on a generalized sobolev space
International Journal of Wavelets Multiresolution and Information Processing, 2017Co-Authors: Mawardi Bahri, Ryuichi AshinoAbstract:The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the Convolution Theorem related to the CFrWT is established using the Convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.
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Correlation formulation using relationship between Convolution and correlation in linear canonical transform domain
2017 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR), 2017Co-Authors: Mawardi Bahri, Amir Kamal Amir, Ryuichi AshinoAbstract:The Convolution Theorem for the linear canonical transformation is introduced. Correlation Theorems related to the linear canonical transformation are established by using the relation between Convolution and correlation definitions in the linear canonical transform domains.
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Two-dimensional quaternion Fourier transform of type II and quaternion wavelet transform
2012 International Conference on Wavelet Analysis and Pattern Recognition, 2012Co-Authors: Mawardi Bahri, Ryuichi Ashino, Rémi VaillancourtAbstract:A two-dimensional quaternion Fourier transform (QFT) defined with the kernel e - i+j+k/√3 ω · x is proposed. Some fundamental properties, such as Convolution Theorem and Plancherel Theorem are established. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.
Rafael Robles - One of the best experts on this subject based on the ideXlab platform.
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the Convolution Theorem for the continuous wavelet tranform
Signal Processing, 2004Co-Authors: Antonio F Perezrendon, Rafael RoblesAbstract: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.