The Hodge De Rham Laplacian And Lp Boundedness Of Riesz Transforms On Non Compact Manifolds
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Analysis of the Hodge Laplacian on the Heisenberg Group
Author | : Detlef Muller |
Publisher | : American Mathematical Soc. |
Total Pages | : 104 |
Release | : 2014-12-20 |
Genre | : Mathematics |
ISBN | : 1470409399 |
The authors consider the Hodge Laplacian \Delta on the Heisenberg group H_n, endowed with a left-invariant and U(n)-invariant Riemannian metric. For 0\le k\le 2n+1, let \Delta_k denote the Hodge Laplacian restricted to k-forms. In this paper they address three main, related questions: (1) whether the L^2 and L^p-Hodge decompositions, 1
Riesz Transform Estimates in the Absence of a Preservation Condition and Applications to the Dirichlet Laplacian
Author | : Joshua Grahame Peate |
Publisher | : |
Total Pages | : 182 |
Release | : 2015 |
Genre | : Dirichlet forms |
ISBN | : |
On Necessary and Sufficient Conditions for $L^p$-Estimates of Riesz Transforms Associated to Elliptic Operators on $\mathbb {R}^n$ and Related Estimates
Author | : Pascal Auscher |
Publisher | : American Mathematical Soc. |
Total Pages | : 108 |
Release | : 2007 |
Genre | : Mathematics |
ISBN | : 9780821839416 |
This memoir focuses on $Lp$ estimates for objects associated to elliptic operators in divergence form: its semigroup, the gradient of the semigroup, functional calculus, square functions and Riesz transforms. The author introduces four critical numbers associated to the semigroup and its gradient that completely rule the ranges of exponents for the $Lp$ estimates. It appears that the case $p2$ which is new. The author thus recovers in a unified and coherent way many $Lp$ estimates and gives further applications. The key tools from harmonic analysis are two criteria for $Lp$ boundedness, one for $p2$ but in ranges different from the usual intervals $(1,2)$ and $(2,\infty)$.
Annales Scientifiques de L'École Normale Supérieure
Author | : École normale supérieure (France) |
Publisher | : |
Total Pages | : 1040 |
Release | : 2004 |
Genre | : Electronic journals |
ISBN | : |
Eigenfunctions of the Laplacian on a Riemannian Manifold
Author | : Steve Zelditch |
Publisher | : American Mathematical Soc. |
Total Pages | : 410 |
Release | : 2017-12-12 |
Genre | : Mathematics |
ISBN | : 1470410370 |
Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.
Elliptic Operators, Topology, and Asymptotic Methods
Author | : John Roe |
Publisher | : Longman Scientific and Technical |
Total Pages | : 208 |
Release | : 1988 |
Genre | : Mathematics |
ISBN | : |