Lieb–Thirring Inequalities for Jacobi Matrices
Copyright policy )Lieb–Thirring Inequalities for Jacobi Matrices
For a Jacobi matrix J on l^2(Z_+) with Ju(n)=a_{n-1} u(n-1) + b_n u(n) + a_n u(n+1), we prove that \sum_{|E|>2} (E^2 -4)^{1/2} \leq \sum_n |b_n| + 4\sum_n |a_n -1|. We also prove bounds on higher moments and some related results in higher dimension.
21 pages, LaTeX2e
- California Institute of Technology United States
Schrödinger operator, Mathematics(all), Numerical Analysis, Applied Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), 510, Miscellaneous inequalities involving matrices, Jacobi matrix, eigenvalue, Difference operators, Analysis, Mathematical Physics
Schrödinger operator, Mathematics(all), Numerical Analysis, Applied Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), 510, Miscellaneous inequalities involving matrices, Jacobi matrix, eigenvalue, Difference operators, Analysis, Mathematical Physics
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