{"user_id":"85821","citation":{"ieee":"M. Kolb and D. Krejčiřík, “Spectral analysis of the diffusion operator with random jumps from the boundary,” <i>Mathematische Zeitschrift</i>, vol. 284, pp. 877–900, 2016, doi: <a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.","ama":"Kolb M, Krejčiřík D. Spectral analysis of the diffusion operator with random jumps from the boundary. <i>Mathematische Zeitschrift</i>. 2016;284:877-900. doi:<a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>","bibtex":"@article{Kolb_Krejčiřík_2016, title={Spectral analysis of the diffusion operator with random jumps from the boundary}, volume={284}, DOI={<a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>}, journal={Mathematische Zeitschrift}, publisher={Springer}, author={Kolb, Martin and Krejčiřík, David}, year={2016}, pages={877–900} }","mla":"Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i>, vol. 284, Springer, 2016, pp. 877–900, doi:<a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>.","apa":"Kolb, M., &#38; Krejčiřík, D. (2016). Spectral analysis of the diffusion operator with random jumps from the boundary. <i>Mathematische Zeitschrift</i>, <i>284</i>, 877–900. <a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>","short":"M. Kolb, D. Krejčiřík, Mathematische Zeitschrift 284 (2016) 877–900.","chicago":"Kolb, Martin, and David Krejčiřík. “Spectral Analysis of the Diffusion Operator with Random Jumps from the Boundary.” <i>Mathematische Zeitschrift</i> 284 (2016): 877–900. <a href=\"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf\">https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf</a>."},"date_created":"2022-09-13T07:56:56Z","title":"Spectral analysis of the diffusion operator with random jumps from the boundary","_id":"33343","department":[{"_id":"96"}],"volume":284,"publisher":"Springer","abstract":[{"text":"Using an operator-theoretic framework in a Hilbert-space setting, we perform a\r\ndetailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to\r\nspecific non-self-adjoint connected boundary conditions modelling a random jump from the\r\nboundary to a point inside the interval. In accordance with previous works, we find that all the\r\neigenvalues are real. As the new results, we derive and analyse the adjoint operator, determine\r\nthe geometric and algebraic multiplicities of the eigenvalues, write down formulae for the\r\neigenfunctions together with the generalised eigenfunctions and study their basis properties.\r\nIt turns out that the latter heavily depend on whether the distance of the interior point to the\r\ncentre of the interval divided by the length of the interval is rational or irrational. Finally,\r\nwe find a closed formula for the metric operator that provides a similarity transform of the\r\nproblem to a self-adjoint operator.","lang":"eng"}],"author":[{"last_name":"Kolb","id":"48880","full_name":"Kolb, Martin","first_name":"Martin"},{"first_name":"David","last_name":"Krejčiřík","full_name":"Krejčiřík, David"}],"status":"public","intvolume":"       284","year":"2016","page":"877-900","type":"journal_article","date_updated":"2022-09-13T07:56:59Z","publication":"Mathematische Zeitschrift","doi":"https://link.springer.com/content/pdf/10.1007/s00209-016-1677-y.pdf","publication_status":"published","language":[{"iso":"eng"}]}