Horia Cornean

OS Mathematical Physics October 28 16:00

How to discretize (pseudo)differential operators with operator norm convergence in the mesh size

We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using orthogonal Riesz sequences. The operators are typically a sum of a Fourier multiplier and a multiplicative potential, but also more general pseudodifferential operators are considered. As a side-product, the Hausdorff distance between the spectra of the resolvents of the continuous and discrete operators decays with the same rate in the mesh size as for the norm resolvent estimates. The same result holds for the spectra of the original operators in a local Hausdorff distance. This is joint work with H. Garde and A. Jensen. https://doi.org/10.1007/s00041-021-09876-5