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Volumn 7, Issue 5, 2006, Pages 933-973

Spectral convergence of Quasi-one-dimensional spaces

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EID: 33748090618     PISSN: 14240637     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00023-006-0272-x     Document Type: Article
Times cited : (89)

References (44)
  • 1
    • 0028444852 scopus 로고
    • On the existence of eigenvalues of a divergence-form operator A + λB in a gap of σ(A)
    • [AADH94]
    • [AADH94] S. Alama, M. Avellaneda, P.A. Deift, and R. Hempel, On the existence of eigenvalues of a divergence-form operator A + λB in a gap of σ(A), Asymptotic Anal. 8 (1994), 311-344.
    • (1994) Asymptotic Anal. , vol.8 , pp. 311-344
    • Alama, S.1    Avellaneda, M.2    Deift, P.A.3    Hempel, R.4
  • 2
    • 12044260159 scopus 로고
    • Periodic Schroedinger operators with large gaps and Wannier-Stark ladders
    • [AEL94]
    • [AEL94] J.E. Avron, P. Exner, and Y. Last, Periodic Schroedinger operators with large gaps and Wannier-Stark ladders, Phys. Rev. Lett. 72 (1994), no. 6, 896-899.
    • (1994) Phys. Rev. Lett. , vol.72 , Issue.6 , pp. 896-899
    • Avron, J.E.1    Exner, P.2    Last, Y.3
  • 4
    • 0011159603 scopus 로고    scopus 로고
    • The creation of spectral gaps by graph decoration
    • [AS00]
    • [AS00] M. Aizenman and J.H. Schenker, The creation of spectral gaps by graph decoration, Lett. Math. Phys. 53 (2000), 253-262.
    • (2000) Lett. Math. Phys. , vol.53 , pp. 253-262
    • Aizenman, M.1    Schenker, J.H.2
  • 5
    • 0035608868 scopus 로고    scopus 로고
    • Manifolds and gruphs with slow heat kernel decay
    • [BCG01]
    • [BCG01] M. Barlow, T. Coulhon, and A. Grigor'yan, Manifolds and gruphs with slow heat kernel decay, Invent. Math. 144 (2001), no. 3, 609-649.
    • (2001) Invent. Math. , vol.144 , Issue.3 , pp. 609-649
    • Barlow, M.1    Coulhon, T.2    Grigor'yan, A.3
  • 6
    • 0242266568 scopus 로고    scopus 로고
    • Large gaps in point-coupled periodic systems of manifolds
    • [BEG03]
    • [BEG03] J. Brüning, P. Exner, and V.A. Geyler, Large gaps in point-coupled periodic systems of manifolds, J. Phys. A 36 (2003), no. 17, 4875-4890.
    • (2003) J. Phys. A , vol.36 , Issue.17 , pp. 4875-4890
    • Brüning, J.1    Exner, P.2    Geyler, V.A.3
  • 7
    • 33748079568 scopus 로고    scopus 로고
    • Spectral properties of Schrödinger operators on decorated graphs
    • [BGL05]
    • [BGL05] J. Brüning, V. Geyler, and I. Lobanov, Spectral properties of Schrödinger operators on decorated graphs, Mat. Zametki 77 (2005), no. 1, 152-156.
    • (2005) Mat. Zametki , vol.77 , Issue.1 , pp. 152-156
    • Brüning, J.1    Geyler, V.2    Lobanov, I.3
  • 9
    • 51249184003 scopus 로고
    • The fundamental group and the spectrum of the Laplacian
    • [Br81a]
    • [Br81a] R. Brooks, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv. 56 (1981), 581-598.
    • (1981) Comment. Math. Helv. , vol.56 , pp. 581-598
    • Brooks, R.1
  • 10
    • 0000864917 scopus 로고
    • A relation between growth and the spectrum of the Laplacian
    • [Br81b]
    • [Br81b] _, A relation between growth and the spectrum of the Laplacian, Math. Z. 178 (1981), no. 4, 501-508.
    • (1981) Math. Z. , vol.178 , Issue.4 , pp. 501-508
  • 11
    • 0000746335 scopus 로고    scopus 로고
    • The spectrum of the continuous Laplacian on a graph
    • [Ca97]
    • [Ca97] C. Cattaneo, The spectrum of the continuous Laplacian on a graph, Monatsh. Math. 124 (1997), no. 3, 215-235.
    • (1997) Monatsh. Math. , vol.124 , Issue.3 , pp. 215-235
    • Cattaneo, C.1
  • 12
    • 0001508569 scopus 로고
    • Spectral properties of Neumann Laplacian of horns
    • [DaS92]
    • [DaS92] E.B. Davies and B. Simon, Spectral properties of Neumann Laplacian of horns, Geom. Funct. Anal. 2 (1992), no. 1, 105-117.
    • (1992) Geom. Funct. Anal. , vol.2 , Issue.1 , pp. 105-117
    • Davies, E.B.1    Simon, B.2
  • 13
    • 0002344710 scopus 로고
    • On the approximation numbers of Sobolev embeddings for irregular domains
    • [EvHa89]
    • [EvHa89] W.D. Evans and D.J. Harris, On the approximation numbers of Sobolev embeddings for irregular domains, Quart. J. Math. Oxford Ser. (2) 40 (1989), no. 157, 13-42.
    • (1989) Quart. J. Math. Oxford Ser. (2) , vol.40 , Issue.157 , pp. 13-42
    • Evans, W.D.1    Harris, D.J.2
  • 14
    • 0034259009 scopus 로고    scopus 로고
    • Neumann Laplacians on domains and operators on associated trees
    • [EvS00]
    • [EvS00] W.D. Evans and Y. Saitō, Neumann Laplacians on domains and operators on associated trees, Q. J. Math. 51 (2000), no. 3, 313-342.
    • (2000) Q. J. Math. , vol.51 , Issue.3 , pp. 313-342
    • Evans, W.D.1    Saito, Y.2
  • 15
    • 0000274654 scopus 로고
    • Lattice Kronig-Penney models
    • [E95]
    • [E95] P. Exner, Lattice Kronig-Penney models, Phys. Rev. Lett. 74 (1995), no. 18, 3503-3506.
    • (1995) Phys. Rev. Lett. , vol.74 , Issue.18 , pp. 3503-3506
    • Exner, P.1
  • 16
    • 0001685320 scopus 로고    scopus 로고
    • A duality between Schrödinger operators on graphs and certain Jacobi matrices
    • [E97]
    • [E97] _, A duality between Schrödinger operators on graphs and certain Jacobi matrices, Ann. Inst. H. Poincaré Phys. Théor. 66 (1997), no. 4, 359-371.
    • (1997) Ann. Inst. H. Poincaré Phys. Théor. , vol.66 , Issue.4 , pp. 359-371
  • 17
    • 16244421065 scopus 로고    scopus 로고
    • Convergence of spectra of graph-like thin manifolds
    • [EP05]
    • [EP05] P. Exner and O. Post, Convergence of spectra of graph-like thin manifolds, Journal of Geometry and Physics 54 (2005), 77-115.
    • (2005) Journal of Geometry and Physics , vol.54 , pp. 77-115
    • Exner, P.1    Post, O.2
  • 19
    • 0000448654 scopus 로고    scopus 로고
    • Schrödinger operators with strong magnetic fields: Quasi-periodicity of spectral orbits and topology
    • [HeN99] American Mathematical Society.
    • [HeN99] I. Herbst and S. Nakamura, Schrödinger operators with strong magnetic fields: Quasi-periodicity of spectral orbits and topology, American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 189(41) (1999), 105-123.
    • (1999) Transl., Ser. 2, Am. Math. Soc. , vol.189 , Issue.41 , pp. 105-123
    • Herbst, I.1    Nakamura, S.2
  • 20
    • 19944380220 scopus 로고
    • First-order asymptotics of the principal eigenvalue of tubular neighborhoods
    • [KaP88] Ithaca, N.Y.
    • [KaP88] L. Karp and M. Pinsky, First-order asymptotics of the principal eigenvalue of tubular neighborhoods, Geometry of random motion (Ithaca, N.Y., 1987)
    • (1987) Geometry of Random Motion
    • Karp, L.1    Pinsky, M.2
  • 21
    • 33748085804 scopus 로고
    • Amer. Math. Soc., Providence, RI
    • Contemp. Math., vol. 73, Amer. Math. Soc., Providence, RI, 1988, pp. 105-119.
    • (1988) Contemp. Math. , vol.73 , pp. 105-119
  • 22
    • 0033613617 scopus 로고    scopus 로고
    • Kirchhoff's rule for quantum wires
    • [KoS99]
    • [KoS99] V. Kostrykin and R. Schrader, Kirchhoff's rule for quantum wires, J. Phys. A 32 (1999), no. 4, 595-630.
    • (1999) J. Phys. A , vol.32 , Issue.4 , pp. 595-630
    • Kostrykin, V.1    Schrader, R.2
  • 24
    • 0036804366 scopus 로고    scopus 로고
    • Graph models for waves in thin structures
    • [Ku02]
    • [Ku02] P. Kuchment, Graph models for waves in thin structures, Waves Random Media 12 (2002), no. 4, R1-R24.
    • (2002) Waves Random Media , vol.12 , Issue.4
    • Kuchment, P.1
  • 25
    • 0942278598 scopus 로고    scopus 로고
    • Quantum graphs: I. Some basic structures
    • [Ku04]
    • [Ku04] _, Quantum graphs: I. Some basic structures, Waves Random Media 14 (2004), S107-S128.
    • (2004) Waves Random Media , vol.14
  • 26
    • 19944375123 scopus 로고    scopus 로고
    • Quantum graphs. II. Some spectral properties of quantum and combinatorial graphs
    • [Ku05]
    • [Ku05] _, Quantum graphs. II. Some spectral properties of quantum and combinatorial graphs, J. Phys. A 38 (2005), no. 22, 4887-4900.
    • (2005) J. Phys. A , vol.38 , Issue.22 , pp. 4887-4900
  • 27
    • 0035877564 scopus 로고    scopus 로고
    • Convergence of spectra of mesoscopic systems collapsing onto a graph
    • [KuZ01]
    • [KuZ01] P. Kuchment and H. Zeng, Convergence of spectra of mesoscopic systems collapsing onto a graph, J. Math. Anal. Appl. 258 (2001), no. 2, 671-700.
    • (2001) J. Math. Anal. Appl. , vol.258 , Issue.2 , pp. 671-700
    • Kuchment, P.1    Zeng, H.2
  • 28
    • 33748038123 scopus 로고    scopus 로고
    • Asymptotics of spectra of Neumann Laplacians in thin domains
    • [KuZ03], Birmingham, AL
    • [KuZ03] _, Asymptotics of spectra of Neumann Laplacians in thin domains, Advances in differential equations and mathematical physics (Birmingham, AL, 2002)
    • (2002) Advances in Differential Equations and Mathematical Physics
  • 29
    • 16244386019 scopus 로고    scopus 로고
    • Amer. Math. Soc., Providence, RI
    • Contemp. Math., vol.327, Amer. Math. Soc., Providence, RI, 2003, pp. 199-213.
    • (2003) Contemp. Math. , vol.327 , pp. 199-213
  • 30
    • 0035315395 scopus 로고    scopus 로고
    • On the spectrum of a finite-volume negatively-curved manifold
    • [Lo01]
    • [Lo01] J. Lott, On the spectrum of a finite-volume negatively-curved manifold, Amer. J. Math. 123 (2001), no. 2, 185-205.
    • (2001) Amer. J. Math. , vol.123 , Issue.2 , pp. 185-205
    • Lott, J.1
  • 33
    • 84972530010 scopus 로고
    • A note on curvature and fundamental group
    • [M68]
    • [M68] J. Milnor, A note on curvature and fundamental group, J. Differential Geometry 2 (1968), 1-7.
    • (1968) J. Differential Geometry , vol.2 , pp. 1-7
    • Milnor, J.1
  • 35
    • 0346361628 scopus 로고    scopus 로고
    • Eigenvalues in spectral gaps of a perturbed periodic manifold
    • [P03a]
    • [P03a] O. Post, Eigenvalues in spectral gaps of a perturbed periodic manifold, Mathematische Nachrichten 261-262 (2003), 141-162.
    • (2003) Mathematische Nachrichten , vol.261-262 , pp. 141-162
    • Post, O.1
  • 36
    • 0037219901 scopus 로고    scopus 로고
    • Periodic manifolds with spectral gaps
    • [P03b]
    • [P03b] _, Periodic manifolds with spectral gaps, J. Diff. Equations 187 (2003), 23-45.
    • (2003) J. Diff. Equations , vol.187 , pp. 23-45
  • 37
    • 19944422439 scopus 로고    scopus 로고
    • Branched quantum wave guides with Dirichlet boundary conditions: The decoupling case
    • [P05]
    • [P05] _, Branched quantum wave guides with Dirichlet boundary conditions: the decoupling case, Journal of Physics A: Mathematical and General 38 (2005), no. 22, 4917-4931.
    • (2005) Journal of Physics A: Mathematical and General , vol.38 , Issue.22 , pp. 4917-4931
  • 38
    • 0001592294 scopus 로고
    • Free-electron network model for conjugated systems, I. Theory
    • [RuS53]
    • [RuS53] K. Ruedenberg and C.W. Scherr, Free-electron network model for conjugated systems, I. Theory, J. Chem. Phys. 21 (1953), 1565-1581.
    • (1953) J. Chem. Phys. , vol.21 , pp. 1565-1581
    • Ruedenberg, K.1    Scherr, C.W.2
  • 40
    • 0035624180 scopus 로고    scopus 로고
    • Variational problems on multiply connected thin strips. I. Basic estimates and convergence of the Laplacian spectrum
    • [RS01]
    • [RS01] J. Rubinstein and M. Schatzman, Variational problems on multiply connected thin strips. I. Basic estimates and convergence of the Laplacian spectrum, Arch. Ration. Mech. Anal. 160 (2001), no. 4, 271-308.
    • (2001) Arch. Ration. Mech. Anal. , vol.160 , Issue.4 , pp. 271-308
    • Rubinstein, J.1    Schatzman, M.2
  • 41
    • 52849138874 scopus 로고    scopus 로고
    • The limiting equation for Neumann Laplacians on shrinking domains
    • [Sa00]
    • [Sa00] Y. Saitō, The limiting equation for Neumann Laplacians on shrinking domains., Electron. J. Differ. Equ. 31 (2000), 25p.
    • (2000) Electron. J. Differ. Equ. , vol.31
    • Saito, Y.1
  • 42
    • 0000604124 scopus 로고    scopus 로고
    • Spectral analysis on infinite Sierpiński gaskets
    • [T98]
    • [T98] A. Teplyaev, Spectral analysis on infinite Sierpiński gaskets, J. Funct. Anal. 159 (1998), no. 2, 537-567.
    • (1998) J. Funct. Anal. , vol.159 , Issue.2 , pp. 537-567
    • Teplyaev, A.1
  • 43
    • 0001489944 scopus 로고
    • Generic properties of eigenfunctions
    • [U76]
    • [U76] K. Uhlenbeck, Generic properties of eigenfunctions, Amer. J. Math. 98 (1976), no. 4, 1059-1078.
    • (1976) Amer. J. Math. , vol.98 , Issue.4 , pp. 1059-1078
    • Uhlenbeck, K.1


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