Use of complex potentials in solving boundary-value problems of the nonlinear theory of hereditary elasticity

1971 ◽  
Vol 7 (10) ◽  
pp. 1156-1159 ◽  
Author(s):  
�. L. Tochilin
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Theory ◽  
Boundary Value ◽  
Complex Potentials ◽  
Hereditary Elasticity

scholarly journals On Compressed Resolvents of Schrödinger Operators with Complex Potentials

2020 ◽  
Vol 15 (1) ◽  
Author(s):  
Jussi Behrndt
Keyword(s):  
Boundary Value Problems ◽  
Operator Theory ◽  
Boundary Value ◽  
Schrödinger Operators ◽  
Complex Potentials ◽  
The Self ◽  
Coupling Method ◽  
Type Formula ◽  
Abstract Operator ◽  
Theory Framework

AbstractThe compression of the resolvent of a non-self-adjoint Schrödinger operator $$-\Delta +V$$ - Δ + V onto a subdomain $$\Omega \subset {\mathbb {R}}^n$$ Ω ⊂ R n is expressed in a Kreĭn–Naĭmark type formula, where the Dirichlet realization on $$\Omega $$ Ω , the Dirichlet-to-Neumann maps, and certain solution operators of closely related boundary value problems on $$\Omega $$ Ω and $${\mathbb {R}}^n\setminus {\overline{\Omega }}$$ R n \ Ω ¯ are being used. In a more abstract operator theory framework this topic is closely connected and very much inspired by the so-called coupling method that has been developed for the self-adjoint case by Henk de Snoo and his coauthors.

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