Approximation of the Hilbert Transform On The Unit Circle
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Scientific Computing"
DOI: 10.1007/s10915-025-03044-3
Abstract: The paper deals with the numerical approximation of the Hilbert transform on the unit circle using Szegő and anti-Szegő quadrature formulas. These schemes exhibit maximum precision with oppositely signed errors and allow for improved accuracy… read more here.
Keywords: hilbert; hilbert transform; transform unit; approximation hilbert ... See more keywords
High degree simple partial fractions in the Bergman space: Approximation and Optimization
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DOI: 10.1007/s13324-025-01145-8
Abstract: We consider the class of standard weighted Bergman spaces Aα2(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A^2_{\alpha }(\mathbb {D})$$\end{document} and the set SFN(T)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SF^N(\mathbb {T})$$\end{document}… read more here.
Keywords: document; simple partial; high degree; usepackage ... See more keywords
Weighted Fekete Points on the Real Line and the Unit Circle
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DOI: 10.1007/s40315-020-00317-w
Abstract: Weighted Fekete points are defined as those that maximize the weighted version of the Vandermonde determinant over a fixed set. They can also be viewed as the equilibrium distribution of the unit discrete charges in… read more here.
Keywords: weighted fekete; real line; unit circle; fekete points ... See more keywords
Optimal tracking and disturbance rejection with invariant zeros on the unit circle: a polynomial spectral factorization design
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DOI: 10.1016/j.ifacol.2017.08.174
Abstract: Abstract We present a simple algorithm for computation of H 2 -optimal tracking and disturbance rejection controller of discrete-time systems possessing invariant zeros on the unit circle, based on polynomial spectral factorization. We prove that… read more here.
Keywords: zeros unit; unit circle; disturbance rejection; tracking disturbance ... See more keywords
Random Bernstein–Markov factors
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2018.12.061
Abstract: For a polynomial $P_n$ of degree $n$, Bernstein's inequality states that $\|P_n'\| \le n \|P_n\|$ for all $L^p$ norms on the unit circle, $0 read more here.
Keywords: vert; vert vert; value vert; unit circle ... See more keywords
R type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle
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DOI: 10.1016/j.laa.2018.10.005
Abstract: We consider a sequence of polynomials $\{P_n\}_{n \geq 0}$ satisfying a special $R_{II}$ type recurrence relation where the zeros of $P_n$ are simple and lie on the real line. It turns out that the polynomial… read more here.
Keywords: type recurrence; unit circle; eigenvalue problem; recurrence ... See more keywords
Experimental investigation of the unit circle minimum variance distortionless response adaptive beamformer
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DOI: 10.1121/1.5014477
Abstract: Source masking occurs when loud interferers produce high side lobes in the conventional beamformer (CBF) scanned response, obscuring the true direction-of-arrival of the desired signal. The minimum variance distortionless response (MVDR) adaptive beamformer (ABF) places… read more here.
Keywords: beamformer; response; unit; unit circle ... See more keywords
Grounding mathematics in an integrated conceptual structure, part I: experimental evidence that grounded rules support transfer that formal rules do not
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DOI: 10.3389/fpsyg.2025.1507670
Abstract: Mathematics relies on formal systems of rules that can be treated in isolation or grounded in a conceptual system that provides meaning for the relationships the rules express. Here, we show how the conceptual system… read more here.
Keywords: structure; formal rules; mathematics; circle ... See more keywords
A Fractional Integration Model and Testing Procedure with Roots Within the Unit Circle
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DOI: 10.3390/math13182978
Abstract: In this paper we propose a statistical model that combines both autoregressions and fractional differentiation in a unified treatment. However, instead of imposing that the roots are strictly on the unit circle, we also allow… read more here.
Keywords: within unit; model; unit circle; fractional integration ... See more keywords
Nonlinear Aggregation of Phase Elements on the Unit Circle under Parametric External Fields
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DOI: 10.7566/jpsj.94.114003
Abstract: We investigate nonlinear aggregation dynamics of phase elements distributed on the unit circle under parametrically modulated external fields. Our model, inspired by flaky particle rotation in fluids, employs the equation ${d\alpha/dt} = \lambda(t)\sin 2(\alpha -… read more here.
Keywords: phase elements; aggregation; nonlinear aggregation; external fields ... See more keywords