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Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...
Existence of Spherically Symmetric Initial Data with Zero Energy, Unit Mass, and Virial less than - 1/2 for the Relativistic Vlasov-Poisson Equation with Attractive Coupling
Zero Energy Unit Mass
2010/11/19
In a recent paper, Kiessling and Tahvildar-Zadeh proved that any spherically symmetric classical solution of the attractive relativistic Vlasov-Poisson equation launched by sufficiently regular initi...
Auto-tuning unit norm frames
frames finite tight unit norm frame potential gradient descent
2010/12/14
Finite unit norm tight frames provide Parseval-like decompositions of vectors in terms of redundant components of equal weight. They are known to be exceptionally robust against additive noise and era...
Rigidity Theorem of Hypersurfaces with Constant Scalar Curvature in a Unit Sphere
principal curvature Clifford torus Gauss equations
2007/12/12
In this paper, we give a characterization of tori $S^1\left(\sqrt{\frac{nr+2-n}{nr}}\right)\times S^{n-1}\left(\sqrt{\frac{n-2}{nr}}\right)$ and $S^m\left(\sqrt{\frac{m}{n}}\right)\times S^{n-m}\left(...
The Isometric Extension of the into Mapping from the Unit Sphere $S(l^\infty_{(2)})$ to $S(L^1(\mu))^1$
isometric mapping isometric extension
2007/12/12
This is the first paper to consider the isometric extension problem of an into-mapping between the unit spheres of two different types of spaces. We prove that, under some conditions, an into-isometri...