Spectral Theory

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3 domain-specific abstractions whose origin domain is Spectral Theory.

• Birman–Schwinger Principle — Turn a perturbed-operator eigenvalue question into a fixed-threshold eigenvalue question for a resolvent-sandwiched auxiliary operator, preserving eigenspace and counting information under stated hypotheses.
• Jacobi operator — A self-adjoint or symmetric tridiagonal operator on a sequence space determined by positive off-diagonal and real diagonal coefficient sequences.
• Riesz projector — A contour-integral projection onto the invariant spectral subspace associated with an isolated portion of an operator’s spectrum.