In this paper, we consider a matrix operator H(l,V)u=(-Δ)^l u+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=(x_1,x_2,…,x_d)∈R^d, d≥2, 1/2.<1>
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper, we consider a matrix operator H(l,V)u=(-Δ)^l u+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=(x_1,x_2,…,x_d)∈R^d, d≥2, 1/2.<1>
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Key Findings & Data:In this paper, we consider a matrix operator H(l,V)u=(-Δ)^l u+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=(x_1,x_2,…,x_d)∈R^d, d≥2, 1/2.<1>
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Conclusion & Impact:In this paper, we consider a matrix operator H(l,V)u=(-Δ)^l u+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=(x_1,x_2,…,x_d)∈R^d, d≥2, 1/2.<1>
In this paper, we consider a matrix operator H(l,V)u=(-Δ)^l u+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=(x_1,x_2,…,x_d)∈R^d, d≥2, 1/2.<1>
Özet
Bu çalışmada, x=(x_1,x_2,…,x_d)∈R^d, d≥2, s≥2, 1/2H(l,q)u=(-Δ)^l u+V(x)u ,matris operatörünün resonans olmayan özdeğerleri için keyfi dereceden asimptotik formülleri elde edilmiştir. Bu gösterimde; (-Δ)^l dioganal elemanları skaler poliharmonik operatör olan diagonal s×s matris, potansiyel V(x) keyfi bir lattise göre periodik ve simetrik bir s×s matristir <1>.
KARAKILIÇ, S. (2020). Polyharmonik Bir Matris Operatörün Rezonans Olmayan Özdeğerinin Pertürbasyonu. Dokuz Eylül Üniversitesi Mühendislik Fakültesi Fen ve Mühendislik Dergisi, Cilt: 22 - Sayı: 66, 725–733. https://ajindex.com/articles/222207
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