On the eigenvalues of a polyharmonic matrix operator near diffraction planes

On the eigenvalues of a polyharmonic matrix operator near diffraction planes

In this study, we consider the d-dimensional polyharmonic matrix operator H(l,V)u=(−Δ)lu+V(x)u, where (−Δ)l is a diagonal s×s matrix, whose diagonal elements are the scalar polyharmonic operators, V is the operator of multiplication by a symmetric s×s matrix, V(x) is periodic with respect to an arbi...

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Hauptverfasser: KARAKILIÇ, Sedef, AKDUMAN, Setenay
Format: Tagungsbericht
Sprache:eng
Schlagworte:
Diffraction
Eigenvalues
Mathematical analysis
Matrix methods
Multiplication
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Beschreibung
Zusammenfassung:In this study, we consider the d-dimensional polyharmonic matrix operator H(l,V)u=(−Δ)lu+V(x)u, where (−Δ)l is a diagonal s×s matrix, whose diagonal elements are the scalar polyharmonic operators, V is the operator of multiplication by a symmetric s×s matrix, V(x) is periodic with respect to an arbitrary lattice and s ≥ 2, x=(x1,x2,⋯,xd)∈ℝd, d≥2,12
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0040407