Hardy—Littlewood—Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs
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DOI: 10.1007/s10114-019-8417-2
Abstract: The purpose of this paper is five-fold. First, we employ the harmonic analysis techniques to establish the following Hardy-Littlewood-Sobolev inequality with the fractional Poisson kernel on the upper half space $$\int_{\mathbb{R}_ + ^n} {{{\int_{\partial \mathbb{R}_… read more here.
Keywords: fractional poisson; hardy littlewood; mathbb; littlewood sobolev ... See more keywords
A kind regularization method with Poisson kernel to solve Cauchy problem of Schrödinger equation
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DOI: 10.1080/00207160.2024.2402906
Abstract: In this work, a precise regularization technique based on the mollification method is proposed to solve the ill-posed Schr $ \ddot {o} $ o¨dinger Cauchy problem with potential-free field. In the sense of Hadamard, this… read more here.
Keywords: method; regularization method; poisson kernel; cauchy problem ... See more keywords
Poisson Kernel-Based Clustering on the Sphere: Convergence Properties, Identifiability, and a Method of Sampling
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DOI: 10.1080/10618600.2020.1740713
Abstract: ABSTRACT Spherical or directional data arise in many applications of interest. Furthermore, many nondirectional datasets can be usefully re-expressed in the form of directions and analyzed as spherical data. We have proposed a clustering algorithm… read more here.
Keywords: kernel based; method; clustering sphere; based clustering ... See more keywords