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Global Green’s Function Estimates

  • Michael W. Frazier
  • Igor E. Verbitsky
Chapter
Part of the International Mathematical Series book series (IMAT, volume 13)

Abstract

Under certain conditions, we obtain global pointwise estimates for Neumann series associated with an integral operator with general quasimetric kernel. The estimates involve the first and second iterations of the original kernel. As a consequence we deduce sharp bilateral bounds of Green's function for the fractional Schrödinger operator (− Δ)α/2 −q with general attractive potential q ≥ 0 on the entire Euclidean space \(\mathbb{R}^n\) for 0 < α < n, or a bounded nontangentially accessible domain \(\Omega \subseteq \mathbb{R}^n \) for 0 < α ≤ 2, under a certain “smallness condition” on q. Most of our results are new even in the classical case α = 2.

Keywords

Bounded Domain Measure Space Lipschitz Domain Euclidean Ball Doubling Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of TennesseeKnoxvilleUSA
  2. 2.Department of MathematicsUniversity of MissouriColumbiaUSA

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