Abstract
A class of operators with special spectral properties is defined. An operator in this class is fairly simple, acts in a separable Hilbert space, and can be perturbed so that an a priori given function from its domain is an eigenfunction of the perturbed operator. This fact is shown to be useful for constructing operators in mathematical physics. Specific examples are given.
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References
Higher Transcendental Functions (Bateman Manuscript Project), Ed. by A. Erdelyi (McGraw-Hill, New York, 1953; Nauka, Moscow, Nauka, Moscow, 1974), Vol. 2.
E. M. Maleko, “Representation of an Operator with a Prescribed Eigenfunction,” Vestn. Magnitogorsk. Gos. Univ. Mat., No. 9, 64–69 (2006).
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E. M. Maleko, Calculation of Spectra of Discrete and Directionally Perturbed Operators (Magnitogorsk. Gos. Univ., Magnitogorsk, 2007).
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Original Russian Text © E.M. Maleko, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 7, pp. 1179–1199.
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Maleko, E.M. On the calculation of the spectra of directionally perturbed operators. Comput. Math. and Math. Phys. 50, 1120–1140 (2010). https://doi.org/10.1134/S096554251007002X
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DOI: https://doi.org/10.1134/S096554251007002X