A MATLAB implementation for computing spectral measures of self-adjoint operators [1] written by Matt Colbrook and Andrew Horning. The code supports
(1) Differential operators on the real line, with variable coefficients,
(2) Integral operators on [-1,1], with smooth kernels,
(3) Infinite matrices, with finite bandwidth or rapid off-diagonal decay [2].
(4) General function handles for computing the resolvent and inner products.
See Example_*.m files for several examples that appear in [1]. SpecSolve functions diffMeas(), intMeas(), and rseMeas() make use of the Chebfun software package for computing with functions, available for download at https://www.chebfun.org/.
Computes a smoothed approximation to the spectral measure of an ordinary, linear differential operator L acting on functions on the real line. L has the form L = a_0 + a_1 D_1 + ... + a_p D_p where D_k is the kth derivative operator and a_k=a_k(x) is a smooth variable coefficient.
Computes a smoothed approximation to the spectral measure of a linear integral operator L acting on functions on [-1,1]. L has the form [Lu](x) = a(x)u(x) + \int K(x,y)u(y) dy where a(x) and K(x,y) are smooth functions on [-1,1] and [-1,1]^2, respectively.
Computes a smoothed approximation to the spectral measure of a lattice operator A acting on square summable sequences.
Computes a smoothed approximation to the spectral measure of radial Schrodinger operators. See Example_radialSchrodinger.m for a worked example.
Computes a smoothed approximation to the spectral measure given function handles for the resolvent and inner products.
[1] M. J. Colbrook, A. Horning, and A. Townsend. "Computing spectral measures of self-adjoint operators." arXiv preprint arXiv:2006.01766v1, 2020.
[2] M. J. Colbrook. "Computing spectral measures and spectral types." arXiv preprint arXiv:1908.06721v2, 2019.