On the spectrum of an infinite-order differential operator and its relation to Hamiltonian mechanics
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Seyed Ebrahim Akrami
Abstract
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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Articles in the same Issue
- Frontmatter
- On nonlinear neutral Liouville–Caputo-type fractional differential equations with Riemann–Liouville integral boundary conditions
- On the spectrum of an infinite-order differential operator and its relation to Hamiltonian mechanics
- Uniqueness of meromorphic functions of differential polynomials sharing a small function with finite weight
- Opial-type inequalities for conformable fractional integrals
- Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex
- Certain inequalities of meromorphic univalent functions associated with the Mittag-Leffler function
- Analytical and asymptotic evaluations of Dawson’s integral and related functions in mathematical physics
- Generalized multivariate Fink-type identity and some related results on time scales with applications
- Best approximation and fixed points for rational-type contraction mappings
- Traveling wave solutions and conservation laws of a generalized Kudryashov–Sinelshchikov equation
Articles in the same Issue
- Frontmatter
- On nonlinear neutral Liouville–Caputo-type fractional differential equations with Riemann–Liouville integral boundary conditions
- On the spectrum of an infinite-order differential operator and its relation to Hamiltonian mechanics
- Uniqueness of meromorphic functions of differential polynomials sharing a small function with finite weight
- Opial-type inequalities for conformable fractional integrals
- Fractional Ostrowski type inequalities for functions whose modulus of the first derivatives are prequasi-invex
- Certain inequalities of meromorphic univalent functions associated with the Mittag-Leffler function
- Analytical and asymptotic evaluations of Dawson’s integral and related functions in mathematical physics
- Generalized multivariate Fink-type identity and some related results on time scales with applications
- Best approximation and fixed points for rational-type contraction mappings
- Traveling wave solutions and conservation laws of a generalized Kudryashov–Sinelshchikov equation
