scholarly journals The generalized Green’s function for an $n$th order linear differential operator

1977 ◽  
Vol 228 ◽  
pp. 243-243
Author(s):  
John Locker
Keyword(s):  
Differential Operator ◽  
Green’S Function ◽  
Green's Function ◽  
Linear Differential Operator ◽  
Order Linear ◽  
Linear Differential

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

2019 ◽  
Vol 25 (2) ◽  
pp. 131-139
Author(s):  
Seyed Ebrahim Akrami
Keyword(s):  
Differential Operator ◽  
Conservation Law ◽  
Infinite Order ◽  
Linear Differential Operator ◽  
Order Differential Operator ◽  
Hamiltonian Mechanics ◽  
Zero Eigenvalue ◽  
Order Linear ◽  
Analytical Functions ◽  
Linear Differential

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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