Neumann series: (I − λK)⁻¹ = Σ λⁿ Kⁿ for |λ|·‖K‖ < 1

Layer 0 — Mathematicsin the integral-equations subtree

Neumann 1877 series expansion of the resolvent operator (I − λK)⁻¹ for a bounded linear operator K with |λ|·‖K‖ < 1: (I − λK)⁻¹ = Σ_{n=0}^{∞} λⁿ·Kⁿ. Applied to integral equations φ = g + λ·Kφ: the resolvent kernel R(x, y; λ) is the…

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