Keldysh's theorem

Keldysh's theorem concerns solutions to certain complex equations, particularly in the context of operator theory. It states that if a linear operator (a mathematical object acting like a function) is close to a well-understood, invertible operator, then they share similar properties—specifically, the number and location of solutions (or eigenvalues). In practical terms, this theorem helps mathematicians predict how small changes in complex systems affect their behavior, ensuring stability in solutions and aiding in the analysis of differential equations and spectral problems.