scholarly journals Similar Operators and a Functional Calculus for the First-Order Linear Differential Operator

1999 ◽  
Vol 22 (1) ◽  
pp. 29-47 ◽  
Author(s):  
David Elizarraraz ◽  
Luis Verde-Star
Keyword(s):  
Differential Operator ◽  
Functional Calculus ◽  
Linear Differential Operator ◽  
Order Linear ◽  
First Order ◽  
Linear Differential

scholarly journals Involutive Property of Resolutions of Differential Operators

1966 ◽  
Vol 27 (2) ◽  
pp. 419-427
Author(s):  
Masatake Kuranishi
Keyword(s):  
Vector Bundle ◽  
Differential Operator ◽  
Vector Space ◽  
Cross Sections ◽  
Vector Bundles ◽  
Differential Operators ◽  
Linear Differential Operator ◽  
First Order ◽  
Linear Differential

Let E and E′ be C∞ vector bundles over a C∞ manifold M. Denote by Γ(E) (resp. by Γ(E′) the vector space of C∞ cross-sections of E (resp. of E′) over M. Take a linear differential operator of the first order D: Γ(E) → Γ(E′) induced by a vector bundle mapping σ(D): jl(E) ′ E′, where Jk(E) denotes the vector bundle of k-jets of cross-sections of E.

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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