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Abelian Theorems for the Real Weierstrass Transform over Compactly Supported Distributions
MathematicsThis paper explores Abelian theorems associated with the real Weierstrass transform over distributions of compact support. This study contributes to both mathematical analysis and distribution theory by offering new insights into the interaction between ...
Benito J. González +2 more
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The Gabor wave front set of compactly supported distributions [PDF]
, 2019 We show that the Gabor wave front set of a compactly supported distribution equals zero times the projection on the second variable of the classical wave front ...
A Weinstein +14 more
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Generators for Rings of Compactly Supported Distributions [PDF]
Integral Equations and Operator Theory, 2010 Let $C$ denote a closed convex cone $C$ in $\mathbb{R}^d$ with apex at 0. We denote by $\mathcal{E}'(C)$ the set of distributions having compact support which is contained in $C$. Then $\mathcal{E}'(C)$ is a ring with the usual addition and with convolution.
Amol Sasane, Sara Maad Sasane
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Compactly supported multi-refinable distributions and B-splines
Journal of Mathematical Analysis and Applications, 2006 Let \(\lambda >0\) and \(\mu >0\) be given. A compactly supported distribution \(\varphi\) is called \(\lambda\)-refinable, if \[ \varphi(x)=\sum_{j=-\infty}^{\infty} c_j\,\varphi( \lambda x - d_j), \] where \(\{j\in {\mathbb Z}; \,c_j\neq 0\}\) is finite and \[ \sum_{j=-\infty}^{\infty} c_j= \lambda. \] If \(\varphi\) is both \(\lambda\)-refinable and
Xin-Rong Dai
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A Characterization of Compactly Supported Both m and n Refinable Distributions
Journal of Approximation Theory, 1999 For \(m\geq 2\), a compactly supported distribution \(\varphi\) is called \(m\) refinable, if \(\varphi(x)= \sum_{j\in\mathbb{Z}} c_j\varphi(mx- j)\) and \(\widehat\varphi(0)= 1\), where \(\sum_{j\in\mathbb{Z}} c_j= m\) and \(c_j\neq 0\) for all but finitely many \(j\in\mathbb{Z}\). Here \(\widehat\varphi\) denotes the Fourier transform of \(\varphi\).
Sun, Qiyu, Zhang, Zeyin
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Compactly supported refinable distributions in Triebel-Lizorkin spaces and besov spaces
Journal of Fourier Analysis and Applications, 1999 This article characterizes compactly supported refinable distributions in Triebel--Lizorkin spaces and Besov spaces by means of projection operators on certain wavelet spaces and by some operators on certain finite dimensional spaces.
Qiyu Sun
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On linear independence of integer shifts of compactly supported distributions
Journal of Approximation Theory, 2016 Compactly supported functions and distributions are used frequently as kernels and other tools for multivariate approximation. In this article, the author gives simple criteria for several of such distributions of compact support (e.g. B-splines, box-splines, etc.) to have linearly independent multi-integer translates.
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ON ONE ZALCMAN PROBLEM FOR THE MEAN VALUE OPERATOR
Ural Mathematical Journal, 2023 Let \(\mathcal{D}'(\mathbb{R}^n)\) and \(\mathcal{E}'(\mathbb{R}^n)\) be the spaces of distributions and compactly supported distributions on \(\mathbb{R}^n\), \(n\geq 2\) respectively, let \(\mathcal{E}'_{\natural}(\mathbb{R}^n)\) be the space of all ...
Natalia P. Volchkova +1 more
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RECOVERING THE LAPLACIAN FROM CENTERED MEANS ON BALLS AND SPHERES OF FIXED RADIUS
Проблемы анализа, 2023 Various issues related to restrictions on radii in meanvalue formulas are well-known in the theory of harmonic functions. In particular, using the Brown-Schreiber-Taylor theorem on spectral synthesis for motion-invariant subspaces in 𝐶(R^𝑛), one can ...
N. P. Volchkova, Vit. V. Volchkov
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Regularity and solutions for flame modelling in porous medium
Results in Physics, 2023 The presented article deals with a model of flame propagation in porous medium. We depart from previously reported models in flame propagation, and we propose a new modelling conception based on a p-Laplacian operator.
José Luis Díaz Palencia +3 more
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