Sharp estimates for Jacobi heat kernels in conic domains

Sharp Pointwise Estimates on Heat Kernels

Characterization of Sharp Global Gaussian Estimates for Schrödinger Heat Kernels

We investigate when the fundamental solution of the Schrödinger equation ∂t = ∆ + V posseses sharp Gaussian bounds global in space and time. We give a characterization for V ≤ 0 and a sufficient condition for general V .

Sharp Estimates for Jacobi Matrices and Chain Sequences

Chain sequences are positive sequences fang of the form an 1⁄4 gnð1 gn 1Þ for a nonnegative sequence fgng: This concept has been introduced by Wall in connection with continued fractions. These sequences are very useful in determining the support of orthogonality measure for orthogonal polynomials. Equivalently, they can be used for localizing spectra of Jacobi matrices associated with orthogon...

Sharp Strichartz Estimates on Non-trapping Asymptotically Conic Manifolds

We obtain the Strichartz inequalities Lt Lx([0,1]×M) ≤ C‖u(0)‖L2(M) for any smooth n-dimensional Riemannian manifold M which is asymptotically conic at infinity (with either short-range or long-range metric perturbation) and non-trapping, where u is a solution to the Schrödinger equation iut + 1 2 ∆Mu = 0, and 2 < q, r ≤ ∞ are admissible Strichartz exponents ( 2 q + n r = n 2 ). This correspond...

Short-time Estimates for Heat Kernels Associated with Root Systems