Chuan-Fu YANG, Zhen-You HUANG, Xiao-Ping YANG

4326

Trace formulae for Schrödinger systems on graphs

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.
Anahtar Kelimeler:

Schrödinger systems, metric graph, d'-type conditions, trace formula, Ambarzumyan-type theorem.

Trace formulae for Schrödinger systems on graphs

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.
Keywords:

Schrödinger systems, metric graph, d'-type conditions, trace formula, Ambarzumyan-type theorem.,

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  • 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
Turkish Journal of Mathematics-Cover
  • ISSN: 1300-0098
  • Yayın Aralığı: Yılda 6 Sayı
  • Yayıncı: TÜBİTAK
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