New Proof of Hörmander multiplier Theorem on compact manifolds without boundary
نویسنده
چکیده
On compact manifolds (M, g) without boundary of dimension n ≥ 2, the gradient estimates for unit band spectral projection operators χλ is proved for any second order elliptic differential operators L by maximum principle. A new proof of Hörmander Multiplier Theorem on the eigenfunction expansion of the operator L is given in this setting by using the gradient estimates and the Calderón-Zygmund argument.
منابع مشابه
Geometric Sampling of Manifolds for Image Representation and Processing
It is often advantageous in image processing and computer vision to consider images as surfaces imbedded in higher dimensional manifolds. It is therefore important to consider the theoretical and applied aspects of proper sampling of manifolds. We present a new sampling theorem for surfaces and higher dimensional manifolds. The core of the proof resides in triangulation results for manifolds wi...
متن کاملSolutions of the Einstein Constraint Equations with Apparent Horizon Boundary
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method introduced by Isenberg for compact manifolds without boundary,suitably extended to accommod...
متن کاملSolutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Isenberg for compact manifolds without boundary, suitably extended to accommodat...
متن کاملOn the Hörmander Multiplier Theorem and Modulation Spaces
Seeger replaced the Sobolev space L2s with s > n/2 appeared in the Hörmander multiplier theorem by the Besov space B n/2 . In this paper, we replace L2s with s > n/2 by the modulation space M 2,1 s with s > 0.
متن کاملThe Basic Theorem and its Consequences
Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...
متن کامل