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.

scholarly journals Ulam Stability of a Second Linear Differential Operator with Nonconstant Coefficients

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1451
Author(s):  
Liviu Cădariu ◽  
Dorian Popa ◽  
Ioan Raşa
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Differential Operator ◽  
Global Solution ◽  
Linear Differential Operator ◽  
Second Order ◽  
Order Differential Operator ◽  
Ulam Stability ◽  
Riccati Differential Equation ◽  
Linear Differential

In this paper, we obtain a result on Ulam stability for a second order differential operator acting on a Banach space. The result is connected to the existence of a global solution for a Riccati differential equation and some appropriate conditions on the coefficients of the operator.

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