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Volumn 14, Issue 2, 2004, Pages 157-183

Analysis of the dispersion equation for the Schrödinger operator on periodic metric graphs

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; BAND STRUCTURE; BINDING ENERGY; CRYSTAL LATTICES; NUMERICAL METHODS; SPECTRUM ANALYSIS;

EID: 1942501049     PISSN: 09597174     EISSN: None     Source Type: Journal    
DOI: 10.1088/0959-7174/14/2/006     Document Type: Article
Times cited : (9)

References (26)
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    • Carlson R 2003 Spectral theory and spectral gaps for periodic Schrödinger operators on product graphs Waves Random Media 14 S29-45
    • (2003) Waves Random Media , vol.14
    • Carlson, R.1
  • 4
    • 0000127775 scopus 로고
    • A scattering problem on noncompact graphs
    • (in Russian)
    • Gerasimenko N and Pavlov B 1988 A scattering problem on noncompact graphs Teor. Mat. Fiz. 74 345-59 (in Russian)
    • (1988) Teor. Mat. Fiz. , vol.74 , pp. 345-359
    • Gerasimenko, N.1    Pavlov, B.2
  • 6
    • 0000201706 scopus 로고
    • An operator generalization of the logarithmic residue theorem and Rouche's theorem
    • (in Russian)
    • Gohberg I S and Sigal E I 1971 An operator generalization of the logarithmic residue theorem and Rouche's theorem Mat. Sb. 94 607-29 (in Russian)
    • (1971) Mat. Sb. , vol.84 , pp. 607-629
    • Gohberg, I.S.1    Sigal, E.I.2
  • 10
    • 0036804366 scopus 로고    scopus 로고
    • Graph models for waves in thin structures
    • Kuchment P 2002 Graph models for waves in thin structures Waves Random Media 12 R1-24
    • (2002) Waves Random Media , vol.12
    • Kuchment, P.1
  • 11
    • 0036109923 scopus 로고    scopus 로고
    • Differential operators on graph and photonic crystal. Modeling and computation in optics and electromagnetics
    • Kuchment P and Kunyansky L 2002 Differential operators on graph and photonic crystal. Modeling and computation in optics and electromagnetics Adv. Comput. Math. 16 263-90
    • (2002) Adv. Comput. Math. , vol.16 , pp. 263-290
    • Kuchment, P.1    Kunyansky, L.2
  • 13
    • 0035530261 scopus 로고    scopus 로고
    • Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators
    • Melnikov Yu and Pavlov B 2001 Scattering on graphs and one-dimensional approximations to N-dimensional Schrödinger operators J. Math. Phys. 42 1202-28
    • (2001) J. Math. Phys. , vol.42 , pp. 1202-1228
    • Melnikov, Y.1    Pavlov, B.2
  • 15
    • 0036070133 scopus 로고    scopus 로고
    • Scattering on a compact domain with few semi-infinite wires attached: Resonance case
    • 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
    • (2002) Math. Nachr. , vol.235 , pp. 101-128
    • Mikhailova, A.1    Pavlov, B.2    Popov, I.3    Rudakova, T.4    Yafyasov, A.5
  • 16
    • 1942445015 scopus 로고
    • Limits on the applicability of the tight-binding approximation method
    • (in Russian)
    • Mironov A and Oleinik V 1994 Limits on the applicability of the tight-binding approximation method Teor. Mat. Fiz. 99 103-20 (in Russian)
    • (1994) Teor. Mat. Fiz. , vol.99 , pp. 103-120
    • Mironov, A.1    Oleinik, V.2
  • 18
    • 1942477291 scopus 로고    scopus 로고
    • On the limits of applicability of the tight binding approximation method for a complex-valued potential
    • (in Russian)
    • 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)
    • (1997) Teor. Mat. Fiz. , vol.112 , pp. 448-466
    • Mironov, A.1    Oleinik, V.2
  • 20
    • 0039103299 scopus 로고
    • Asymptotic behavior of energy band associated with a negative energy level
    • Oleinik V 1990 Asymptotic behavior of energy band associated with a negative energy level. J. Stat. Phys. 59 665-78
    • (1990) J. Stat. Phys. , vol.59 , pp. 665-678
    • Oleinik, V.1
  • 21
    • 1942445013 scopus 로고    scopus 로고
    • Boundary value problem for Laplacian with data on singular (polar) sets
    • in preparation
    • Oleinik V and Pavlov B 2004 Boundary value problem for Laplacian with data on singular (polar) sets. in preparation
    • (2004)
    • Oleinik, V.1    Pavlov, B.2
  • 23
    • 84934403327 scopus 로고
    • Spectral properties of one-dimensional disperse crystals. Differential geometry, Lie groups and mechanics
    • (in Russian)
    • 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)
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    • Pavlov, B.1    Smirnov, N.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.