The asymptotic behavior of the spectral function of an operator in Lp with discrete spectrum

1994 ◽  
Vol 69 (3) ◽  
pp. 1065-1067
Author(s):  
V. A. Sadovnichii ◽  
V. V. Dubrovskii ◽  
A. V. Nagornyi
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Function ◽  
Discrete Spectrum

Asymptotic behavior of the spectral function of an operator family

1997 ◽  
Vol 61 (5) ◽  
pp. 664-668
Author(s):  
A. S. Pechentsov ◽  
A. Yu. Popov
Keyword(s):  
Asymptotic Behavior ◽  
Spectral Function ◽  
Operator Family

scholarly journals Asymptotics for Helmholtz and Maxwell Solutions in 3-D Open Waveguides

2012 ◽  
Vol 11 (2) ◽  
pp. 629-646 ◽  
Author(s):  
Carlos Jerez-Hanckes ◽  
Jean-Claude Nédélec
Keyword(s):  
Asymptotic Behavior ◽  
Discrete Spectrum ◽  
Electromagnetic Fields ◽  
Three Dimensions ◽  
Guided Modes ◽  
Open Waveguides ◽  
Radiation Conditions

AbstractWe extend classic Sommerfeld and Silver-Müller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three dimensions. If X= (x1,x2,x3)ϵℝ3, with x3 denoting the direction orthogonal to the layers, standard conditions only hold for the outer layers in the region ∣x3∣ > ∣∣x∣γ, for γϵ(1/4,1/2) and x large. For ∣x3∣ < ∣∣x∣∣γ and inside the slab, asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

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