Results 1 
8 of
8
SubGaussian estimates of heat kernels on infinite graphs
 Duke Math. J
, 2000
"... We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay. ..."
Abstract

Cited by 30 (10 self)
 Add to MetaCart
We prove that a two sided subGaussian estimate of the heat kernel on an infinite weighted graph takes place if and only if the volume growth of the graph is uniformly polynomial and the Green kernel admits a uniform polynomial decay.
Maximal inequalities and Riesz transform estimates on L p spaces for Schrödinger operators with nonnegative potentials
, 2006
"... We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
We show various L p estimates for Schrödinger operators −∆+V on R n and their square roots. We assume reverse Hölder estimates on the potential, and improve some results of Shen [Sh1]. Our main tools are improved FeffermanPhong inequalities and reverse Hölder estimates for weak solutions of − ∆ + V and their gradients.
Riesz transform on manifolds and Poincaré inequalities
, 2005
"... We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities. ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
We study the validity of the L p inequality for the Riesz transform when p> 2 and of its reverse inequality when p < 2 on complete Riemannian manifolds under the doubling property and some Poincaré inequalities.
Harmonic analysis related to Schrödinger operators, arXiv:0711.3262v1. 24 W. Schlag, A remark on LittlewoodPaley theory for the distorted Fourier transform
 Proc. Amer. Math. Soc
, 2007
"... Abstract. In this article we give an overview on some recent development of LittlewoodPaley theory for Schrödinger operators. We extend the LittlewoodPaley theory for special potentials considered in the authors ’ previous work. We elaborate our approach by considering potential in C ∞ 0 or Schwar ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. In this article we give an overview on some recent development of LittlewoodPaley theory for Schrödinger operators. We extend the LittlewoodPaley theory for special potentials considered in the authors ’ previous work. We elaborate our approach by considering potential in C ∞ 0 or Schwartz class in one dimension. In particular the low energy estimates are treated by establishing some new and refined asymptotics for the eigenfunctions and their Fourier transforms. We give maximal function characterization of the Besov spaces and TriebelLizorkin spaces associated with H. We then prove a spectral multiplier theorem on these spaces and derive Strichartz estimates for the wave equation with a potential. We also consider similar problem for the unbounded potentials in the Hermite and Laguerre cases, whose V = ax  2 + bx  −2 are known to be critical in the study of perturbation of nonlinear dispersive equations. This improves upon the previous results when we apply the upper Gaussian bound for the heat kernel and its gradient. 1.
SOME ESTIMATES OF FUNDAMENTAL SOLUTION ON NONCOMPACT MANIFOLDS WITH TIMEDEPENDENT METRICS
, 810
"... Abstract. In this article, we obtain some further estimates of fundamental solutions comparing to ChauTamYu [1] and give some applications of the estimates on asymptotic behaviors of fundamental solutions. 1. ..."
Abstract
 Add to MetaCart
Abstract. In this article, we obtain some further estimates of fundamental solutions comparing to ChauTamYu [1] and give some applications of the estimates on asymptotic behaviors of fundamental solutions. 1.
CONTENTS
, 2006
"... This draft report provides an initial description of the programming language X10. X10 is a singleinheritance classbased objectoriented (OO) programming language designed for highperformance, highproductivity computing on highend computers supporting ≈ 10 5 hardware threads and ≈ 10 15 operatio ..."
Abstract
 Add to MetaCart
This draft report provides an initial description of the programming language X10. X10 is a singleinheritance classbased objectoriented (OO) programming language designed for highperformance, highproductivity computing on highend computers supporting ≈ 10 5 hardware threads and ≈ 10 15 operations per second. X10 is based on stateoftheart objectoriented programming languages and deviates from them only as necessary to support its design goals. The language is intended to have a simple and clear semantics and be readily accessible to mainstream OO programmers. It is intended to support a wide variety of concurrent programming idioms. This document provides an initial description of the language and corresponds to the first implementation of the language. The X10 design team consists of DAVID BACON, BOB BLAINEY,
Riesz transform on manifolds and heat . . .
, 2004
"... One considers the class of complete noncompact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel s ..."
Abstract
 Add to MetaCart
One considers the class of complete noncompact Riemannian manifolds whose heat kernel satisfies Gaussian estimates from above and below. One shows that the Riesz transform is L p bounded on such a manifold, for p ranging in an open interval above 2, if and only if the gradient of the heat kernel satisfies a certain L p estimate in the same
unknown title
"... quadrature formula for diffusion polynomials corresponding to a generalized heat kernel ..."
Abstract
 Add to MetaCart
quadrature formula for diffusion polynomials corresponding to a generalized heat kernel