Equivalence of the Weighted Fractional Sobolev Space on a Disk with Characterization by the Decay Rate of Fourier–Jacobi Coefficients and K-Interpolation
Sign Up to like & getrecommendations! Published in 2024 at "Journal of Fourier Analysis and Applications"
DOI: 10.1007/s00041-024-10127-6
Abstract: In this paper, motivated by the analysis of the fractional Laplace equation on the unit disk in R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^{2}$$\end{document}, we establish a characterisation of the weighted… read more here.
Keywords: sobolev space; decay rate; rate fourier; fourier jacobi ... See more keywords
Existence of Solutions for p(x)-Laplacian Elliptic BVPs on a Variable Sobolev Space Via Fixed Point Theorems
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DOI: 10.1007/s12346-024-01054-4
Abstract: In this paper, we prove some existence theorems for elliptic boundary value problems within the p ( x )-Laplacian on a variable Sobolev space. For this purpose, the main problem is transformed into a fixed… read more here.
Keywords: sobolev space; variable sobolev; fixed point; point ... See more keywords
L 2-Sobolev space bijectivity of the inverse scattering of a 3 × 3 AKNS system
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DOI: 10.1088/1361-6544/aaf527
Abstract: We study the $L^2$-Sobolev space bijectivity of the direct and inverse scattering of the $3\times 3$ AKNS system associated to the Manakov system and Sasa-Satsuma equation. We establish the bijectivity on the weighted Sobolev space… read more here.
Keywords: system; space; sobolev space; inverse scattering ... See more keywords
Existence results of non-local integro-differential problem with singularity under a new fractional Musielak–Sobolev space
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DOI: 10.1088/1751-8121/adaa3e
Abstract: In this article, we construct a new fractional Musielak–Sobolev space designed to address the non-locality associated with the corresponding integro-differential operators. The completeness, reflexivity, and uniform convexity of this new space, along with an associated… read more here.
Keywords: sobolev space; new fractional; space; fractional musielak ... See more keywords
Differentiability of Mappings of the Sobolev Space Wn−11 with Conditions on the Distortion Function
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DOI: 10.1134/s0037446618060034
Abstract: We define two scales of the mappings that depend on two real parameters p and q, with n−1 ≤ q ≤ p < ∞, as well as a weight function θ. The case q =… read more here.
Keywords: sobolev space; distortion; differentiability mappings; function ... See more keywords
Some Conditions and Perturbation Theorem of Irregular Wavelet/Gabor Frames in Sobolev Space
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DOI: 10.1155/2024/9932668
Abstract: Due to its potential applications in image restoration and deep convolutional neural networks, the study of irregular frames has interested some researchers. This paper addresses irregular wavelet systems (IWSs) and irregular Gabor systems (IGSs) in… read more here.
Keywords: sobolev space; perturbation theorem; gabor; irregular wavelet ... See more keywords
An estimate on the Bedrosian commutator in Sobolev space
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DOI: 10.1186/s13660-018-1940-3
Abstract: While the Bedrosian identity for the Hilbert transform of a product does not hold for general Sobolev class functions, we show that the defect of this identity is more regular than would be naively expected.… read more here.
Keywords: sobolev space; estimate bedrosian; bedrosian commutator; commutator sobolev ... See more keywords
Fractional double-phase nonlocal equation in Musielak-Orlicz Sobolev space
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DOI: 10.1186/s13661-024-01877-9
Abstract: In this paper, we analyze the existence of solutions to a double-phase fractional equation of the Kirchhoff type in Musielak-Orlicz Sobolev space with variable exponents. Our approach is mainly based on the sub-supersolution method and… read more here.
Keywords: equation; sobolev space; musielak orlicz; orlicz sobolev ... See more keywords
Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications
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DOI: 10.3390/a18070374
Abstract: The optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas. It is known that the… read more here.
Keywords: sobolev space; quadrature; quadrature formulas; weighted optimal ... See more keywords
The Fuzzy Width Theory in the Finite-Dimensional Space and Sobolev Space
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DOI: 10.3390/math11102331
Abstract: This paper aims to fuzzify the width problem of classical approximation theory. New concepts of fuzzy Kolmogorov n-width and fuzzy linear n-width are introduced on the basis of α-fuzzy distance which is induced by the… read more here.
Keywords: finite dimensional; space; dimensional space; width ... See more keywords