Essential Spectrum of Discrete Laplacian – Revisited

• Autores: V.B. Kiran Kumar
• Localización: 3 c TIC: cuadernos de desarrollo aplicados a las TIC, ISSN-e 2254-6529, Vol. 11, Nº. 2, 2022, págs. 52-59
• Idioma: inglés
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• Resumen

  • Consider the discrete Laplacian operator A acting on l2(Z). It is well known from the classical literature that the essential spectrum of A is a compact interval. In this article, we give an elementary proof for this result, using the finite-dimensional truncations An of A. We do not rely on symbol analysis or any infinite-dimensional arguments. Instead, we consider the eigenvalue-sequences of the truncations An and make use of the filtration techniques due to Arveson. Usage of such techniques to the discrete Schrödinger operator and to the multi-dimensional settings will be interesting future problems.