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On the spectrum of an infinite-order differential operator and its relation to Hamiltonian mechanics

Journal of Applied Analysis, ISSN: 1869-6082, Vol: 25, Issue: 2, Page: 131-139
2019
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Article Description

We introduce an infinite-order linear differential operator and study its spectrum. We show that all analytical functions around the origin are its eigenfunctions corresponding to zero eigenvalue. We outline an interesting relation between this operator and the conservation law of energy in Hamiltonian mechanics.

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