We present an example of linear differential operator in a Hilbert space, which has no eigenfunctions but has, in a certain sense, some generalized eigenfunctions. It is proved that this operator is formally adjoint to Bessel-type differential operators for which the systems of canonical eigenfunctions are over-complete. We also analyze the completeness of the system of generalized eigenfunctions for this differential operator.
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Translated from Neliniini Kolyvannya, Vol. 25, No. 2-3, pp. 242–252, April–September, 2022.
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Khats’, R.V. Completeness of the System of Generalized Eigenfunctions for a Bessel-Type Differential Operator. J Math Sci 274, 898–911 (2023). https://doi.org/10.1007/s10958-023-06652-2
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DOI: https://doi.org/10.1007/s10958-023-06652-2