Equilibrium measures and capacities in spectral theory

B Simon - arXiv preprint arXiv:0711.2700, 2007 - arxiv.org
This is a comprehensive review of the uses of potential theory in studying the spectral theory
of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular …

Diffusion and mixing in fluid flow

P Constantin, A Kiselev, L Ryzhik, A Zlatoš - Annals of Mathematics, 2008 - JSTOR
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast
incompressible flow. Our main result is a sharp description of the class of flows that make the …

[PDF][PDF] Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators

Y Last, B Simon - arXiv preprint math-ph/9907023, 1999 - arxiv.org
arXiv:math-ph/9907023v1 28 Jul 1999 Page 1 arXiv:math-ph/9907023v1 28 Jul 1999
EIGENFUNCTIONS, TRANSFER MATRICES, AND ABSOLUTELY CONTINUOUS SPECTRUM …

[图书][B] Real analysis

B Simon - 2015 - books.google.com
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume
set that can serve as a graduate-level analysis textbook with a lot of additional bonus …

On the Absolutely Continuous Spectrum¶ of One-Dimensional Schrödinger Operators¶ with Square Summable Potentials

P Deift, R Killip - Communications in mathematical physics, 1999 - Springer
For continuous and discrete one-dimensional Schrödinger operators with square summable
potentials, the absolutely continuous part of the spectrum is essentially supported by [0,∞) …

Schrödinger operators in the twentieth century

B Simon - Journal of Mathematical Physics, 2000 - pubs.aip.org
Schrödinger operators in the twentieth century | Journal of Mathematical Physics | AIP
Publishing Skip to Main Content Umbrella Alt Text Umbrella Alt Text Close Publishers AIP …

Spectral theory of Sturm-Liouville operators on infinite intervals: a review of recent developments

Y Last - Sturm-Liouville Theory: Past and Present, 2005 - Springer
This review discusses some of the central developments in the spectral theory of Sturm-
Liouville operators on infinite intervals over the last thirty years or so. We discuss some of …

Eigenvalue statistics for CMV matrices: from Poisson to clock via random matrix ensembles

R Killip, M Stoiciu - 2009 - projecteuclid.org
We study CMV matrices (discrete one-dimensional Dirac-type operators) with random
decaying coefficients. Under mild assumptions, we identify the local eigenvalue statistics in …

The absolutely continuous spectrum of Jacobi matrices

C Remling - Annals of mathematics, 2011 - JSTOR
I explore some consequences of a groundbreaking result of Breimesser and Pearson on the
absolutely continuous spectrum of one-dimensional Schrödinger operators. These include …

Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: some optimal results

M Christ, A Kiselev - Journal of the American Mathematical Society, 1998 - ams.org
The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to
be stable under perturbation by potentials satisfying mild decay conditions. In particular, the …