scholarly journals Propagation Through Trapped Sets and Semiclassical Resolvent Estimates

2012 ◽  
pp. 7-10
Author(s):  
Kiril Datchev ◽  
András Vasy
Keyword(s):  
Resolvent Estimates

scholarly journals Eigenvalue bounds for non-selfadjoint Dirac operators

2021 ◽  
Author(s):  
Piero D’Ancona ◽  
Luca Fanelli ◽  
Nico Michele Schiavone
Keyword(s):  
Dirac Operator ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Dirac Operators ◽  
Resolvent Estimates ◽  
Eigenvalue Bounds ◽  
Mixed Norms ◽  
Massless Case ◽  
Abstract Version ◽  
Embedded Eigenvalues

AbstractWe prove that the eigenvalues of the n-dimensional massive Dirac operator $${\mathscr {D}}_0 + V$$ D 0 + V , $$n\ge 2$$ n ≥ 2 , perturbed by a potential V, possibly non-Hermitian, are contained in the union of two disjoint disks of the complex plane, provided V is sufficiently small with respect to the mixed norms $$L^1_{x_j} L^\infty _{{\widehat{x}}_j}$$ L x j 1 L x ^ j ∞ , for $$j\in \{1,\dots ,n\}$$ j ∈ { 1 , ⋯ , n } . In the massless case, we prove instead that the discrete spectrum is empty under the same smallness assumption on V, and in particular the spectrum coincides with the spectrum of the unperturbed operator: $$\sigma ({\mathscr {D}}_0+V)=\sigma ({\mathscr {D}}_0)={\mathbb {R}}$$ σ ( D 0 + V ) = σ ( D 0 ) = R . The main tools used are an abstract version of the Birman–Schwinger principle, which allows in particular to control embedded eigenvalues, and suitable resolvent estimates for the Schrödinger operator.

scholarly journals $N$ -body resolvent estimates

1996 ◽  
Vol 48 (1) ◽  
pp. 135-160 ◽  
Author(s):  
Christian GÉRARD ◽  
Hiroshi ISOZAKI ◽  
Erik SKIBSTED
Keyword(s):  
Resolvent Estimates

scholarly journals Semiclassical resolvent estimates for Hölder potentials

2020 ◽  
Vol 2 (4) ◽  
pp. 841-860
Author(s):  
Georgi Vodev
Keyword(s):  
Resolvent Estimates

scholarly journals Applications of Cutoff Resolvent Estimates to the Wave Equation

2009 ◽  
Vol 16 (4) ◽  
pp. 577-590 ◽  
Author(s):  
Hans Christianson
Keyword(s):  
Wave Equation ◽  
Resolvent Estimates
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