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A Spherical Harmonic Expansion of the Hilbert Transform on the Two-Sphere

机译：双球面上Hilbert变换的球面调和展开式

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Oliver Fleischmann; Lennart Wietzke; Gerald Sommer;
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年度 2015
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1. Recovering functions from the spherical mean transform with limited radii data by expansion into spherical harmonics [J] . Salman Yehonatan Journal of Mathematical Analysis and Applications . 2018,第1期

机译：通过扩展到球形谐波，从球形平均转换从球形平均转换中恢复功能
2. Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series [J] . Slevinsky Richard Mikael Applied and Computational Harmonic Analysis . 2019,第3期

机译：球谐函数展开与二元傅里叶级数之间的快速和向后稳定变换
3. APS -Joint Fall 2017 Meeting of the Texas Section of the APS, Texas Section of the AAPT, and Zone 13 of the Society of Physics Students- Event - The Global Gravity Gradient Field of the Planet Mars Determined using a Spherical Harmonic Expansion and the Fourier Transform: A Comparative Analysis [J] . Juan Hinojosa Bulletin of the American Physical Society . 2017,第16期

机译：APS-APS得克萨斯分校，AAPT得克萨斯分校和物理学生学会第13区的2017年秋季联合会议-事件-使用球谐展开和傅里叶确定的火星全球重力梯度场转换：比较分析
4. A Spherical Harmonic Expansion of the Hilbert Transform on the Two-Sphere [C] . Oliver Fleischmann, Lennart Wietzke, Gerald Sommer International Conference on Numerical Analysis and Applied Mathematics . 2009

机译：双球上的Hilbert变换的球形谐波膨胀
5. Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space. [D] . Donnelly, Roderick Kerry. 1988

机译：对分析的一些贡献：涉及Hilbert变换的积分微分方程的广义函数的新空间，以及关于Hilbert空间上测试函数的空间的非核性的注释。
6. Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients [O] . Juan Manuel Solano-Altamirano, Alejandro Vázquez-Otero, Danila Khikhlukha, 2017

机译：使用球谐函数扩展从梯度重建光学表面
7. Fast and backward stable transforms between spherical harmonic expansions and bivariate Fourier series [O] . Slevinsky, Richard Mikael 2017

机译：球谐波之间的快速和后向稳定变换扩展和双变量傅里叶级数
8. Computation of Spherical Harmonics and Approximation by Spherical Harmonic Expansions [R] . Freeden, W. 1985

机译：球谐函数的球谐函数计算及近似

A Spherical Harmonic Expansion of the Hilbert Transform on the Two-Sphere

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