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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 2, Pages 17–23
DOI: https://doi.org/10.4213/faa3070 (Mi faa3070) 		 
A Formula for the Spectra of Differential Operators on Graphs

R. S. Ismagilov

N. E. Bauman Moscow State Technical University
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DOI: https://doi.org/10.4213/faa3070
Abstract: We consider a connected undirected finite graph and a spectral problem generated by the double differentiation of functions on its edges (under usual conditions on the vertices ensuring the self-adjointness of the problem). We introduce, in a standard way, an entire function vanishing at the nonzero eigenvalues of the problem and give an explicit formula for this function, which involves graphs (introduced by V. I. Arnold) generated by a self-mapping of a finite set.
Keywords: differential operators, spectra, graph, cycle, tree.
Received: 03.11.2011
English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 2, Pages 94–99
DOI: https://doi.org/10.1007/s10688-012-0015-3
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: R. S. Ismagilov, “A Formula for the Spectra of Differential Operators on Graphs”, Funktsional. Anal. i Prilozhen., 46:2 (2012), 17–23; Funct. Anal. Appl., 46:2 (2012), 94–99
Citation in format AMSBIB
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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