scholarly journals On the equivalence of Green functions for general Schrödinger operators on a half-space

2004 ◽  
Vol 83 (1) ◽  
pp. 65-76
Author(s):  
Abdoul Ifra ◽  
Lotfi Riahi
Keyword(s):  
Half Space ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Green Functions

scholarly journals On-diagonal singularities of the Green functions for Schrödinger operators

2005 ◽  
Vol 46 (11) ◽  
pp. 113508 ◽  
Author(s):  
Jochen Brüning ◽  
Vladimir Geyler ◽  
Konstantin Pankrashkin
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Green Functions

scholarly journals Decay rates at infinity for solutions to periodic Schrödinger equations

2019 ◽  
Vol 150 (3) ◽  
pp. 1113-1126
Author(s):  
Daniel M. Elton
Keyword(s):  
Half Space ◽  
Absolute Continuity ◽  
Evolution Equations ◽  
Schrödinger Operators ◽  
Decay Rates ◽  
Schrodinger Equations ◽  
Schrodinger Operators ◽  
Schrödinger Equations ◽  
The Absolute ◽  
Continuity Of The Spectrum

AbstractWe consider the equation Δu = Vu in the half-space ${\open R}_ + ^d $, d ⩾ 2 where V has certain periodicity properties. In particular, we show that such equations cannot have non-trivial superexponentially decaying solutions. As an application this leads to a new proof for the absolute continuity of the spectrum of particular periodic Schrödinger operators. The equation Δu = Vu is studied as part of a broader class of elliptic evolution equations.

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