On Discrete Spectrum of a Model Graph with Loop and Small Edges

نویسندگان

چکیده

We consider a perturbed graph consisting of two infinite edges, loop, and glued arbitrary finite γε with small where is obtained by ε−1 times contraction some fixed ε parameter. On the graph, we Schrödinger operator whose potential on edges can singularly depend Kirchhoff condition at internal vertices Dirichlet or Neumann boundary vertices. For eigenvalue corresponding eigenfunction prove holomorphy respect to propose recurrent algorithm for finding all coefficients their Taylor series.

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ژورنال

عنوان ژورنال: Journal of Mathematical Sciences

سال: 2021

ISSN: ['1072-3374', '1573-8795']

DOI: https://doi.org/10.1007/s10958-021-05503-2