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Journals / Turkish Journal of Mathematics / 2010 / Cilt: 34 - Sayı: 2

Trace formulae for Schrödinger systems on graphs

Chuan-Fu YANG
Zhen-You HUANG
Xiao-Ping YANG
Pages
181–196
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:For Schrödinger systems on metric graphs with d'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term.
📊
Key Findings & Data:Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis.
💡
Conclusion & Impact:Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Schrödinger systems · metric graph · d'-type conditions

Abstract

For Schrödinger systems on metric graphs with d'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

Özet

For Schrödinger systems on metric graphs with d'-type conditions at the central vertex, firstly, we obtain precise description for the square root of the large eigenvalue up to the o(1/n)-term. Secondly, the regularized trace formulae for Schrödinger systems are calculated with some techniques in classical analysis. Finally, these formulae are used to obtain a result of inverse problem in the spirit of Ambarzumyan.

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Cite This Article

YANG, C., HUANG, Z., YANG, X. (2022). Trace formulae for Schrödinger systems on graphs. Turkish Journal of Mathematics, Cilt: 34 - Sayı: 2, 181–196. https://ajindex.com/articles/608539

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References (1)

  1. Thus, the right hand side of (5.2) is exactly 0, the test function Yk,0makes the functional (A2Y, Y )/||Y ||2 achieve its minimum value and is thus the Şrst eigenfunction. Substituting Yk,0into the equation (2.1), we obtain qj(x) = 0, j = 1, 2,· · ·, d. The proof is Şnished. 2