87 citations · 337 across the 24 of their papers we have counts for
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math.SP2001★ 2 cited
Quasi-conformal mappings and periodic spectral problems in dimension two
E. Shargorodsky, A. V. Sobolev
We study spectral properties of second order elliptic operators with periodic coefficients in dimension two. These operators act in periodic simply-connected waveguides, with eithe…
math.SP2001★ 71 cited
Schrödinger operator on homogeneous metric trees: spectrum in gaps
A. V. Sobolev, M. Solomyak
The paper studies the spectral properties of the Schrödinger operator on a homogeneous rooted metric tree, with a decaying real-valued potential and a coupl…