# Spectral analysis of the diffusion operator with random jumps from the boundary

@article{Kolb2015SpectralAO, title={Spectral analysis of the diffusion operator with random jumps from the boundary}, author={M. Kolb and D. Krej{\vc}iř{\'i}k}, journal={Mathematische Zeitschrift}, year={2015}, volume={284}, pages={877-900} }

Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specific non-self-adjoint connected boundary conditions modelling a random jump from the boundary to a point inside the interval. In accordance with previous works, we find that all the eigenvalues are real. As the new results, we derive and analyse the adjoint operator, determine the geometric and algebraic multiplicities… CONTINUE READING

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