Elementary linear algebra for advanced spectral problems

2003/12/08 by Johannes Sjoestrand, Sjoestrand, J., Maciej Zworski +1 · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #35Q40 #35R99 #46N40 #65N25 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0312166

openalex publication_date 2003/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the general method of Grushin problems, closely related to Shur complements, Feshbach projections and effective Hamiltonians, and describe various appearances in spectral theory, pdes, mathematical physics and numerical problems.

Cited by

• The strength of weak coupling
• Boundary spectral behaviour for semiclassical operators in one dimension
• Spectral properties of random perturbations of non-normal Toeplitz matrices
• Relative convergence estimates for the spectral asymptotic in the Large Coupling Limit

Related

• Sharp spectral multipliers for a new class of Grushin type operators
• Shape perturbation of Grushin eigenvalues
• Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis
• Spectral problems from quantum field theory
• Spectral analysis of Grushin type operators on the quarter plane