References
- Ansel'm , A I . 1978 . Introduction to the Theory of Semiconductors , Moscow : Nauka . (in Russian)
- Bogevolnov , V , Mikhailova , A , Pavlov , B and Yafyasov , A . 2001 . “ About scattering on the ring ” . In Operator Theory: Advances and Application , vol 124 , 155 – 87 . Basel : Birkhauser .
- Carlson , R . 2003 . Spectral theory and spectral gaps for periodic Schrödinger operators on product graphs . Waves Random Media , 14 : S29 – 45 .
- Gerasimenko , N and Pavlov , B . 1988 . A scattering problem on noncompact graphs . Teor. Mat. Fiz. , 74 : 345 – 59 . (in Russian)
- Gerasimenko , N and Pavlov , B . 1988 . Theor. Math. Phys. , 74 : 230 – 40 . (Engl. Transl.)
- Gohberg , I S and Sigal , E I . 1971 . An operator generalization of the logarithmic residue theorem and Rouché's theorem . Mat. Sb. , 84 : 607 – 29 . (in Russian)
- Gohberg , I S and Sigal , E I . 1971 . Math. USSR-Sb. , 13 : 603 – 25 . (Engl. Transl.)
- Gorbachuk , V I and Gorbachuk , M L . 1991 . Boundary Value Problems for Operator Differential Equations , Dordrecht : Kluwer .
- Kostrykin , V and Schrader , R . 1999 . Kirchhoff's rule for quantum wires . J. Phys. A: Math. Gen. , 32 : 595 – 630 .
- Kuchment , P . 2002 . Graph models for waves in thin structures . Waves Random Media , 12 : R1 – 24 .
- Kuchment , P and Kunyansky , L . 2002 . Differential operators on graph and photonic crystals. Modeling and computation in optics and electromagnetics . Adv. Comput. Math. , 16 : 263 – 90 .
- Lebedev , D and Oleinik , V . Spectrum band asymptotics of Schrödinger operator in model domain with periodic structure . June 1998 , St Petersburg, Russia. Proc. Int. Seminar ‘Day on Diffraction 98’ , pp. 82 – 5 .
- Melnikov , Yu and Pavlov , B . 2001 . Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators . J. Math. Phys. , 42 : 1202 – 28 .
- Mikhailova , A and Oleinik , V . 2000 . Tight-binding investigation of the generalized Dirac comb . June 2000 , St Petersburg, Russia. Proc. Int. Seminar ‘Day on Diffraction 2000’ , pp. 95 – 107 .
- Mikhailova , A , Pavlov , B , Popov , I , Rudakova , T and Yafyasov , A . 2002 . Scattering on a compact domain with few semi-infinite wires attached: resonance case . Math. Nachr. , 235 : 101 – 28 .
- Mironov , A and Oleinik , V . 1994 . Limits on the applicability of the tight-binding approximation method . Teor. Mat. Fiz. , 99 : 103 – 20 . (in Russian)
- Mironov , A and Oleinik , V . 1994 . Theor. Math. Phys. , 99 : 457 – 69 . (Engl. Transl.)
- Mironov , A and Oleinik , V . 1997 . On the limits of applicability of the tight binding approximation method for a complex-valued potential . Teor. Mat. Fiz. , 112 : 448 – 66 . (in Russian)
- Mironov , A and Oleinik , V . 1997 . Theor. Math. Phys. , 112 : 1157 – 71 . (Engl. Transl.)
- Oleinik , V . 1990 . Asymptotic behavior of energy band associated with a negative energy level . J. Stat. Phys. , 59 : 665 – 78 .
- Oleinik , V and Pavlov , B . 2004 . Boundary value problem for Laplacian with data on singular (polar) sets in preparation .
- Oleinik , V and Sibirev , N . Asymptotics of localized spectral bands of the periodical waveguide . June 2002 , St Petersburg, Russia. Proc. Int. Seminar ‘Day on Diffraction 2002’ , pp. 94 – 102 .
- Pavlov , B and Smirnov , N . 1984 . Spectral properties of one-dimensional disperse crystals. Differential geometry, Lie groups and mechanics, VI . Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) , 133 : 197 – 211 . (in Russian)
- Pavlov , B and Smirnov , N . 1985 . J. Sov. Math. , 31 : 3388 – 98 . (Engl. Transl.)
- Pavlov , B . 2001 . “ S-matrix and Dirichlet-to-Neumann operators ” . In Scattering: Scattering and Inverse Scattering in Pure and Applied Science , 1678 – 88 . New York : Academic .
- Sylvester , J and Uhlmann , G . The Dirichlet to Neumann map and applications . Proc. Conf. Inverse Problems in Partial Differential Equations (Arcata, 1989) , pp. 101 – 39 . Philadelphia, PA : SIAM .