scholarly journals Generating Eigenvalue Bounds Using Optimization

2009 ◽  
pp. 465-490 ◽  
Author(s):  
Henry Wolkowicz
Keyword(s):  
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

Eigenvalue bounds for Orr-Sommerfeld equation ‘No backward wave’ theorem

1996 ◽  
Vol 106 (3) ◽  
pp. 281-287 ◽  
Author(s):  
Mihir B Banerjee ◽  
R G Shandil ◽  
Balraj Singh Bandral
Keyword(s):  
Eigenvalue Bounds ◽  
Backward Wave ◽  
Sommerfeld Equation

scholarly journals Eigenvalue bounds for the signless laplacian

2007 ◽  
pp. 11-27 ◽  
Author(s):  
Dragos Cvetkovic ◽  
Peter Rowlinson ◽  
Slobodan Simic
Keyword(s):  
Previous Survey ◽  
Eigenvalue Bounds ◽  
Largest Eigenvalue ◽  
Signless Laplacian

We extend our previous survey of properties of spectra of signless Laplacians of graphs. Some new bounds for eigenvalues are given, and the main result concerns the graphs whose largest eigenvalue is maximal among the graphs with fixed numbers of vertices and edges. The results are presented in the context of a number of computer-generated conjectures.

Note on eigenvalue bounds for the Orr-Sommerfeld equation

1969 ◽  
Vol 38 (2) ◽  
pp. 273-278 ◽  
Author(s):  
Chia-Shun Yih
Keyword(s):  
Boundary Conditions ◽  
Wave Velocity ◽  
Channel Flow ◽  
Eigenvalue Bounds ◽  
Complex Wave ◽  
Sommerfeld Equation

Bounds for the complex wave velocity c, determined by the Orr-Sommerfeld equation and the boundary conditions for channel flow, have been given by Joseph (1968a,b). In these notes it is shown how two of Joseph's theorems can be uniformly improved.

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