Asymptotics of the discrete spectrum of the Dirichlet and Neumann problems on the fundamental domain of the crystallographic group

1989 ◽  
Vol 45 (5) ◽  
pp. 391-395
Author(s):  
L. B. Parnovskii
Keyword(s):  
Discrete Spectrum ◽  
Fundamental Domain ◽  
Crystallographic Group ◽  
Neumann Problems

scholarly journals A zeta function connected with the eigenvalues of the Laplace-Beltrami operator on the fundamental domain of the modular group

1984 ◽  
Vol 96 ◽  
pp. 167-174 ◽  
Author(s):  
Akio Fujii
Keyword(s):  
Zeta Function ◽  
Discrete Spectrum ◽  
Complex Plane ◽  
Fundamental Domain ◽  
Modular Group ◽  
Beltrami Operator

Let ; … run over the eigenvalues of the discrete spectrum of the Laplace-Beltrami operator on L2(H/yΓ), where H is the upper half of the complex plane and we take Γ = PSL(2, Z). It is well known that Let a be a positive number. Here we are concerned with the zeta function defined by

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

Some Aspects of Discrete Relaxation Time Spectra as Obtained from Dynamic Moduli Data

1995 ◽  
Vol 60 (11) ◽  
pp. 1815-1829 ◽  
Author(s):  
Jaromír Jakeš
Keyword(s):  
Relaxation Time ◽  
Least Squares ◽  
Discrete Spectrum ◽  
Integral Transform ◽  
Time Spectrum ◽  
Relaxation Time Spectrum ◽  
Dynamic Moduli ◽  
Best Fitting ◽  
Discrete Spectra ◽  
Well Posed

The problem of finding a relaxation time spectrum best fitting dynamic moduli data in the least-squares sense is shown to be well-posed and to yield a discrete spectrum, provided the data cannot be fitted exactly, i.e., without any deviation of data and calculated values. Properties of the resulting spectrum are discussed. Examples of discrete spectra obtained from simulated literature data and experimental literature data on polymers are given. The problem of smoothing discrete spectra when continuous ones are expected is discussed. A detailed study of an integral transform inversion under the non-negativity constraint is given in Appendix.

Localization of Discrete Spectrum of Multiparticle Schrödinger Operators

1985 ◽  
Vol 40 (10) ◽  
pp. 1052-1058 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Discrete Spectrum ◽  
Lower Bounds ◽  
Upper Bound ◽  
Schrödinger Operators ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

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.

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