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Darrin Speegle - One of the best experts on this subject based on the ideXlab platform.
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Linear Independence of time frequency translates in mathbb r d
Journal of Geometric Analysis, 2016Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time-frequency translates for functions \(f\) on \(\mathbb {R}^d\) having one-sided decay \(\lim _{x \in H,\ |x|\rightarrow \infty } |f(x)| e^{c|x| \log |x|} = 0\) for all \(c>0\), which do not vanish on an affine half-space \(H \subset \mathbb {R}^d\).
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the hrt conjecture and the zero divisor conjecture for the heisenberg group
2015Co-Authors: Christopher Heil, Darrin SpeegleAbstract:This chapter reports on the current status of the HRT Conjecture (also known as the Linear Independence of time–frequency shifts conjecture), and discusses its relationship with a longstanding conjecture in algebra known as the zero divisor conjecture.
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Linear Independence of time frequency translates of functions with faster than exponential decay
Bulletin of The London Mathematical Society, 2013Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time–frequency translates for functions f having onesided decay limx→∞ |f(x)|e cx log x = 0 for all c> 0. We also prove such results for functions with faster than exponential decay, that is, limx→∞ |f(x)|e cx = 0 for all c> 0, under some additional restrictions.
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Linear Independence of time frequency translates of functions with faster than exponential decay
arXiv: Functional Analysis, 2012Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for functions with faster than exponential decay, i.e., $\lim_{x\to \infty} |f(x)| e^{cx} = 0$ for all $c>0$, under some additional restrictions.
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Linear Independence of parseval wavelets
Illinois Journal of Mathematics, 2010Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish several results yielding Linear Independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding Linear Independence is that the space V (ψ) is shiftinvariant. In particular, the affine system generated by a Parseval wavelet is Linearly independent. As an illustration of our techniques, we give an alternative proof of the theorem of Linnell (see Proc. Amer. Math. Soc. 127 (1999), 3269–3277) on Linear Independence of Gabor systems.
Marcin Bownik - One of the best experts on this subject based on the ideXlab platform.
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Linear Independence of time frequency translates in mathbb r d
Journal of Geometric Analysis, 2016Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time-frequency translates for functions \(f\) on \(\mathbb {R}^d\) having one-sided decay \(\lim _{x \in H,\ |x|\rightarrow \infty } |f(x)| e^{c|x| \log |x|} = 0\) for all \(c>0\), which do not vanish on an affine half-space \(H \subset \mathbb {R}^d\).
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Linear Independence of time frequency translates of functions with faster than exponential decay
Bulletin of The London Mathematical Society, 2013Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time–frequency translates for functions f having onesided decay limx→∞ |f(x)|e cx log x = 0 for all c> 0. We also prove such results for functions with faster than exponential decay, that is, limx→∞ |f(x)|e cx = 0 for all c> 0, under some additional restrictions.
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Linear Independence of time frequency translates of functions with faster than exponential decay
arXiv: Functional Analysis, 2012Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish the Linear Independence of time-frequency translates for functions $f$ having one sided decay $\lim_{x\to \infty} |f(x)| e^{cx \log x} = 0$ for all $c>0$. We also prove such results for functions with faster than exponential decay, i.e., $\lim_{x\to \infty} |f(x)| e^{cx} = 0$ for all $c>0$, under some additional restrictions.
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Linear Independence of parseval wavelets
Illinois Journal of Mathematics, 2010Co-Authors: Marcin Bownik, Darrin SpeegleAbstract:We establish several results yielding Linear Independence of the affine system generated by ψ in exchange for conditions on the space V (ψ) of negative dilates. A typical assumption yielding Linear Independence is that the space V (ψ) is shiftinvariant. In particular, the affine system generated by a Parseval wavelet is Linearly independent. As an illustration of our techniques, we give an alternative proof of the theorem of Linnell (see Proc. Amer. Math. Soc. 127 (1999), 3269–3277) on Linear Independence of Gabor systems.
Jose M C Pereira - One of the best experts on this subject based on the ideXlab platform.
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a test for directional Linear Independence with applications to wildfire orientation and size
Stochastic Environmental Research and Risk Assessment, 2014Co-Authors: Eduardo Garciaportugues, Ana M G Barros, Rosa M Crujeiras, Wenceslao Gonzalezmanteiga, Jose M C PereiraAbstract:A nonparametric test for assessing the Independence between a directional random variable (circular or spherical, as particular cases) and a Linear one is proposed in this paper. The statistic is based on the squared distance between nonparametric kernel density estimates and its calibration is done by a permutation approach. The size and power characteristics of various variants of the test are investigated and compared with those for classical correlation-based tests of Independence in an extensive simulation study. Finally, the best-performing variant of the new test is applied in the analysis of the relation between the orientation and size of Portuguese wildfires.
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a test for directional Linear Independence with applications to wildfire orientation and size
arXiv: Methodology, 2013Co-Authors: Eduardo Garciaportugues, Ana M G Barros, Rosa M Crujeiras, Wenceslao Gonzalezmanteiga, Jose M C PereiraAbstract:The relation between wildfire orientation and size is analyzed by means of a nonparametric test for directional-Linear Independence. The test statistic is designed for assessing the Independence between two random variables of different nature, specifically directional (fire orientation, circular or spherical, as particular cases) and Linear (fire size measured as burnt area, scalar), based on a directional-Linear nonparametric kernel density estimator. In order to apply the proposed methodology in practice, a resampling procedure based on permutations and bootstrap is provided. The finite sample performance of the test is assessed by a simulation study, comparing its behavior with other classical tests for the circular-Linear case. Finally, the test is applied to analyze wildfire data from Portugal.
Giancarlo Sangalli - One of the best experts on this subject based on the ideXlab platform.
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analysis suitable t splines of arbitrary degree definition Linear Independence and approximation properties
Mathematical Models and Methods in Applied Sciences, 2013Co-Authors: Beirao L Da Veiga, Annalisa Buffa, Giancarlo Sangalli, Rafael VazquezAbstract:T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear Independence of the blending functions and optimal approximation properties of the associated T-spline space. These are corollaries of our main result: A T-mesh is analysis-suitable if and only if it is dual-compatible. Indeed, dual compatibility is a concept already defined and used in L. Beirao da Veiga et al.5 Analysis-suitable T-splines are dual-compatible which allows for a straightforward construction of a dual basis.
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Linear Independence of the T-spline blending functions associated with some particular T-meshes
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: Annalisa Buffa, Durkbin Cho, Giancarlo SangalliAbstract:Based on the local refinement algorithm addressed in Sederberg et al. (2004) [17], we analyze the Linear Independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.
Annalisa Buffa - One of the best experts on this subject based on the ideXlab platform.
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analysis suitable t splines of arbitrary degree definition Linear Independence and approximation properties
Mathematical Models and Methods in Applied Sciences, 2013Co-Authors: Beirao L Da Veiga, Annalisa Buffa, Giancarlo Sangalli, Rafael VazquezAbstract:T-splines are an important tool in IGA since they allow local refinement. In this paper we define analysis-suitable T-splines of arbitrary degree and prove fundamental properties: Linear Independence of the blending functions and optimal approximation properties of the associated T-spline space. These are corollaries of our main result: A T-mesh is analysis-suitable if and only if it is dual-compatible. Indeed, dual compatibility is a concept already defined and used in L. Beirao da Veiga et al.5 Analysis-suitable T-splines are dual-compatible which allows for a straightforward construction of a dual basis.
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Linear Independence of the T-spline blending functions associated with some particular T-meshes
Computer Methods in Applied Mechanics and Engineering, 2009Co-Authors: Annalisa Buffa, Durkbin Cho, Giancarlo SangalliAbstract:Based on the local refinement algorithm addressed in Sederberg et al. (2004) [17], we analyze the Linear Independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes.