scholarly journals A note on eigenvalue bounds for non‐compact manifolds

2021 ◽  
Author(s):  
Matthias Keller ◽  
Shiping Liu ◽  
Norbert Peyerimhoff
Keyword(s):  
Compact Manifolds ◽  
Eigenvalue Bounds

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 Computable eigenvalue bounds for rank-k perturbations

2010 ◽  
Vol 432 (12) ◽  
pp. 3100-3116 ◽  
Author(s):  
Jan H. Brandts ◽  
Ricardo Reis da Silva
Keyword(s):  
Eigenvalue Bounds

scholarly journals Global branches of periodic solutions for forced delay differential equations on compact manifolds

2007 ◽  
Vol 233 (2) ◽  
pp. 404-416 ◽  
Author(s):  
Pierluigi Benevieri ◽  
Alessandro Calamai ◽  
Massimo Furi ◽  
Maria Patrizia Pera
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Compact Manifolds ◽  
Delay Differential
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