scholarly journals Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs

2019 ◽  
Vol 60 (9) ◽  
pp. 093502 ◽  
Author(s):  
Peter Kuchment ◽  
Jia Zhao
Keyword(s):  
Operator Technique ◽  
Quantum Graphs ◽  
Neumann Operator ◽  
Dirichlet To Neumann Operator

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

scholarly journals The Dirichlet-to-Neumann operator on rough domains

2011 ◽  
Vol 251 (8) ◽  
pp. 2100-2124 ◽  
Author(s):  
W. Arendt ◽  
A.F.M. ter Elst
Keyword(s):  
Neumann Operator ◽  
Dirichlet To Neumann Operator
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