The Correct Definition of Second-Order Elliptic Operators with Point Interactions and their Resolvents

2020 ◽  
Vol 30 (3) ◽  
pp. 153-161
Author(s):  
G. E. Abduakhitova ◽  
B. E. Kanguzhin
Keyword(s):  
Elliptic Operators ◽  
Second Order ◽  
Point Interactions ◽  
Correct Definition ◽  
Definition Of ◽  
Second Order Elliptic Operators

On the spectra of non-self-adjoint realisations of second-order elliptic operators

1981 ◽  
Vol 90 (1-2) ◽  
pp. 71-105 ◽  
Author(s):  
W. D. Evans
Keyword(s):  
Spherical Shell ◽  
Essential Spectrum ◽  
Weighted Space ◽  
Elliptic Operators ◽  
Second Order ◽  
Sectorial Operator ◽  
Image Position ◽  
Second Order Elliptic Operators ◽  
Complex Valued

SynopsisLet τ denote the second-order elliptic expressionwhere the coefficients bj and q are complex-valued, and let Ω be a spherical shell Ω = {x:x ∈ ℝn, l <|x|<m} with l≧0, m≦∞. Under the conditions assumed on the coefficients of τ and with either Dirichlet or Neumann conditions on the boundary of Ω, τ generates a quasi-m-sectorial operator T in the weighted space L2(Ω;w). The main objective is to locate the spectrum and essential spectrum of T. Best possible results are obtained.

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