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Volumn 21, Issue 4, 1997, Pages 337-356

On the spectrum of a random walk on the discrete Heisenberg group and the norm of Harper's operator

Author keywords

Harper operator; Heisenberg group; Random walk

Indexed keywords


EID: 0031101158     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0393-0440(96)00024-1     Document Type: Article
Times cited : (32)

References (32)
  • 1
    • 0001539982 scopus 로고
    • On the measure of the spectrum for the almost Mathieu operator
    • [AMS90] J. Avron, P.H.M.van Mouche and B. Simon, On the measure of the spectrum for the almost Mathieu operator, Commun. Math. Phys. 132 (1990) 103-118.
    • (1990) Commun. Math. Phys. , vol.132 , pp. 103-118
    • Avron, J.1    Van Mouche, P.H.M.2    Simon, B.3
  • 2
    • 84966202323 scopus 로고
    • Singular continuous spectrum for a class of almost periodic Jacobi matrices
    • [AS82] J. Avron and B. Simon, Singular continuous spectrum for a class of almost periodic Jacobi matrices, Bull. Amer. Math. Soc. (New Series) 81-85 (1982).
    • (1982) Bull. Amer. Math. Soc. (New Series) , pp. 81-85
    • Avron, J.1    Simon, B.2
  • 3
    • 0011001797 scopus 로고
    • Geometric K -theory for Lie groups and foliations
    • preprint
    • [BC82] P. Baum and A. Connes, Geometric K -theory for Lie groups and foliations, preprint, IHES (1982).
    • (1982) IHES
    • Baum, P.1    Connes, A.2
  • 4
    • 0001884702 scopus 로고
    • C* -algebras in solid state physics: 2D electrons in a uniform magnetic field
    • eds. D.E. Evans and M. Takesaki (Cambridge University Press, Cambridge)
    • [Bel88] J. Bellissard, C* -algebras in solid state physics: 2D electrons in a uniform magnetic field, in: Operator Algebras and applications eds. D.E. Evans and M. Takesaki, Vol. 2 (Cambridge University Press, Cambridge, 1988) pp. 49-76.
    • (1988) Operator Algebras and Applications , vol.2 , pp. 49-76
    • Bellissard, J.1
  • 5
    • 0002656467 scopus 로고
    • Le papillon de Hofstadter
    • d'après B.Helffer et J.Sjöstrand
    • [Bel91] J. Bellissard, Le papillon de Hofstadter (d'après B.Helffer et J.Sjöstrand), in: Sém. Bourbaki, Exposé 745 (1991).
    • (1991) Sém. Bourbaki, Exposé , vol.745
    • Bellissard, J.1
  • 6
    • 21344486877 scopus 로고
    • Lipschitz continuity of gap boundaries for Hofstadter-like spectra
    • [Bel94] J. Bellissard, Lipschitz continuity of gap boundaries for Hofstadter-like spectra, Commun. Math. Phys. 160 (1994) 599-613.
    • (1994) Commun. Math. Phys. , vol.160 , pp. 599-613
    • Bellissard, J.1
  • 7
    • 0004242420 scopus 로고
    • Cambridge University Press, Cambridge
    • [Big93] N. Biggs, Algebraic Graph Theory (Cambridge University Press, Cambridge, 1993).
    • (1993) Algebraic Graph Theory
    • Biggs, N.1
  • 8
    • 0001391870 scopus 로고
    • Gauss polynomials and the rotation algebra
    • [CEY90] M.-D. Choi, G.A. Eliott and N. Yui, Gauss polynomials and the rotation algebra, Invent. Math. 99 (1990) 225-246.
    • (1990) Invent. Math. , vol.99 , pp. 225-246
    • Choi, M.-D.1    Eliott, G.A.2    Yui, N.3
  • 9
    • 85033103754 scopus 로고    scopus 로고
    • On spectra of simple random walks on one relator groups
    • to appear
    • [CV] P.-A. Cherix and A. Valette, On spectra of simple random walks on one relator groups, Pac. J. Math., to appear.
    • Pac. J. Math.
    • Cherix, P.-A.1    Valette, A.2
  • 10
    • 0003252136 scopus 로고
    • Random walks and electric networks
    • Math. Assoc. Amer.
    • [DS84] P.G. Doyle and J.L. Snell, Random walks and electric networks, Carus Math. Monograph 2, Math. Assoc. Amer. (1984).
    • (1984) Carus Math. Monograph , vol.2
    • Doyle, P.G.1    Snell, J.L.2
  • 11
    • 0000762788 scopus 로고
    • Gaps in the spectrum of an almost periodic Schrödinger operator
    • [E1I82] G.A. Elliott, Gaps in the spectrum of an almost periodic Schrödinger operator, C.R. Math. Rep. Acad. Sci. Canada 4 (1982) 255-259.
    • (1982) C.R. Math. Rep. Acad. Sci. Canada , vol.4 , pp. 255-259
    • Elliott, G.A.1
  • 12
    • 22044432097 scopus 로고    scopus 로고
    • Interlacing eigenvalues and graphs
    • to appear
    • [Hae] W.H. Haemers, Interlacing eigenvalues and graphs, Linear Algebra Appl., to appear.
    • Linear Algebra Appl.
    • Haemers, W.H.1
  • 13
    • 0001032458 scopus 로고
    • Energy levels and waves functions of Bloch electrons in rational and irrational magnetic fields
    • [Hof 76] D.R. Hofstadter, Energy levels and waves functions of Bloch electrons in rational and irrational magnetic fields, Phys. Rev. 14 (1976) 2239-2249.
    • (1976) Phys. Rev. , vol.14 , pp. 2239-2249
    • Hofstadter, D.R.1
  • 14
    • 51249166573 scopus 로고
    • On the spectrum of the sum of generators for a finitely generated group
    • [HRV93a] P.de.la Harpe, A.G. Robertson, and A. Valette, On the spectrum of the sum of generators for a finitely generated group, Israel J. Math. 81 (1993) 65-96.
    • (1993) Israel J. Math. , vol.81 , pp. 65-96
    • De.La Harpe, P.1    Robertson, A.G.2    Valette, A.3
  • 15
    • 0002184804 scopus 로고
    • On the spectrum of the sum of generators for a finitely generated group II
    • [HRV93b] P.de.la Harpe, A.G. Robertson, and A. Valette, On the spectrum of the sum of generators for a finitely generated group II, Collect. Math. LXV (1993) 87-102.
    • (1993) Collect. Math. , vol.65 , pp. 87-102
    • De.La Harpe, P.1    Robertson, A.G.2    Valette, A.3
  • 16
    • 0041070561 scopus 로고
    • Analyse semi-classique pour l'équation de Harper II; comportement semi-classique près d'un rationnel
    • [HS90] B. Helffer and J. Sjöstrand, Analyse semi-classique pour l'équation de Harper II; comportement semi-classique près d'un rationnel, Mémoire de la SMF No. 40 (1990) 118.
    • (1990) Mémoire de la SMF No. 40 , vol.40 , pp. 118
    • Helffer, B.1    Sjöstrand, J.2
  • 17
    • 0003111433 scopus 로고
    • Smooth dense subalgebras of reduced group C*-algebras, Schwartz cohomology of groups, and cyclic cohomology
    • [Ji92] R. Ji, Smooth dense subalgebras of reduced group C*-algebras, Schwartz cohomology of groups, and cyclic cohomology, J. Funct. Anal. 107 (1992) 1-33.
    • (1992) J. Funct. Anal. , vol.107 , pp. 1-33
    • Ji, R.1
  • 18
    • 0010991666 scopus 로고
    • Certain full group C*-algebras without proper projection
    • [JP90] R. Ji and S. Pedersen, Certain full group C*-algebras without proper projection, J. Operator Theory 24 (1990) 239-252.
    • (1990) J. Operator Theory , vol.24 , pp. 239-252
    • Ji, R.1    Pedersen, S.2
  • 19
    • 34250090959 scopus 로고
    • Equivariant K K -theory and the Novikov conjecture
    • [Kas88] G.G. Kasparov, Equivariant K K -theory and the Novikov conjecture, Invent. Math. 91 (1988) 147-201.
    • (1988) Invent. Math. , vol.91 , pp. 147-201
    • Kasparov, G.G.1
  • 20
    • 0000803079 scopus 로고
    • Full Banach mean values on countable groups
    • [Kes59a] H. Kesten, Full Banach mean values on countable groups, Math. Scand. 7 (1959) 146-156.
    • (1959) Math. Scand. , vol.7 , pp. 146-156
    • Kesten, H.1
  • 21
    • 33847574798 scopus 로고
    • Symmetric random walks on groups
    • [Kes59b] H. Kesten, Symmetric random walks on groups, Trans. Amer, Math. Soc. 92 (1959) 336-354.
    • (1959) Trans. Amer, Math. Soc. , vol.92 , pp. 336-354
    • Kesten, H.1
  • 22
    • 0003097742 scopus 로고
    • Projections in C*-algebras of nilpotent groups
    • [KT89] E. Kaniuth and K.F. Taylor, Projections in C*-algebras of nilpotent groups, Manuscripta Math. 65 (1989) 93-111.
    • (1989) Manuscripta Math. , vol.65 , pp. 93-111
    • Kaniuth, E.1    Taylor, K.F.2
  • 23
    • 33847667155 scopus 로고
    • Zero measure spectrum for the almost Mathieu operator
    • [Las94] Y. Last, Zero measure spectrum for the almost Mathieu operator, Commun. Math. Phys. 164 (1994) 421-432.
    • (1994) Commun. Math. Phys. , vol.164 , pp. 421-432
    • Last, Y.1
  • 24
    • 0000445261 scopus 로고
    • 2-invariants by their finite-dimensional analogues
    • 2-invariants by their finite-dimensional analogues, Geom. Funct. Anal. 4 (1994) 455-481.
    • (1994) Geom. Funct. Anal. , vol.4 , pp. 455-481
    • Lück, W.1
  • 25
    • 0002449448 scopus 로고
    • The spectrum of Jacobi matrices
    • [Moe76] P. van Moerbeke, The spectrum of Jacobi matrices, Invent. Math. 37 (1976) 45-81.
    • (1976) Invent. Math. , vol.37 , pp. 45-81
    • Van Moerbeke, P.1
  • 27
    • 0000495523 scopus 로고
    • An algebraic semi-classical approach to Bloch electrons in a magnetic field
    • [RB90] R. Rammal and J. Bellissard, An algebraic semi-classical approach to Bloch electrons in a magnetic field, J. Phys. France 51 (1990) 1803-1830.
    • (1990) J. Phys. France , vol.51 , pp. 1803-1830
    • Rammal, R.1    Bellissard, J.2
  • 28
    • 84972491035 scopus 로고
    • C* -algebras associated with irrational rotations
    • [Rie81] M. Rieffel, C* -algebras associated with irrational rotations, Pacific J. Maths. 93 (1981) 415-429.
    • (1981) Pacific J. Maths. , vol.93 , pp. 415-429
    • Rieffel, M.1
  • 29
    • 0001343595 scopus 로고
    • Noncommutative tori - A case study of non-commutative differentiable manifolds
    • [Rie90] M. Rieffel, Noncommutative tori - a case study of non-commutative differentiable manifolds, Contemp. Math. 105 (1990) 191-211.
    • (1990) Contemp. Math. , vol.105 , pp. 191-211
    • Rieffel, M.1
  • 30
    • 84951601375 scopus 로고
    • C*-algebras, positive scalar curvature and the Novikov conjecture
    • [Ros83] J. Rosenberg, C*-algebras, positive scalar curvature and the Novikov conjecture, Publ. Math. IHES 58 (1983) 197-212.
    • (1983) Publ. Math. IHES , vol.58 , pp. 197-212
    • Rosenberg, J.1
  • 31
    • 0001004549 scopus 로고
    • Discrete magnetic Laplacian
    • [Shu94] M.A. Shubin, Discrete magnetic Laplacian, Commun. Math. Phys. 164 (1994) 259-275.
    • (1994) Commun. Math. Phys. , vol.164 , pp. 259-275
    • Shubin, M.A.1
  • 32
    • 0000257777 scopus 로고
    • The conjecture of idempotents : A survey of the C*-algebraic approach
    • [Val89] A. Valette, The conjecture of idempotents : A survey of the C*-algebraic approach, Bulletin de la Société Mathématique de Belgique XLI (1989) 485-521.
    • (1989) Bulletin de la Société Mathématique de Belgique , vol.41 , pp. 485-521
    • Valette, A.1


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