Sparse block-Jacobi matrices with arbitrarily accurate Hausdorff dimension
Tài liệu tham khảo
Breuer, 2007, Singular continuous spectrum for the Laplacian on certain sparse trees, Comm. Math. Phys., 269, 851, 10.1007/s00220-006-0121-2
Breuer, 2007, Singular continuous and dense point spectrum for sparse trees with finite dimensions, vol. 42, 65
Del Rio, 1996, Operators with singular continuous spectrum, IV. Hausdorff dimension, rank one perturbations and localization, J. Anal. Math., 69, 153, 10.1007/BF02787106
Falconer, 1990
Gesztesy, 2000, On matrix-valued Herglotz functions, Math. Nachr., 218, 61, 10.1002/1522-2616(200010)218:1<61::AID-MANA61>3.0.CO;2-D
Gilbert, 1987, On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators, J. Math. Anal. Appl., 128, 30, 10.1016/0022-247X(87)90212-5
Jitomirskaya, 1999, Power-law subordinacy and singular spectra I. Half-line operators, Acta Math., 183, 171, 10.1007/BF02392827
Kiselev, 1998, Modified Prüfer and EFGP transforms and the spectral analysis of one-dimensional Schrödinger operators, Comm. Math. Phys., 194, 1, 10.1007/s002200050346
Krutikov, 2001, Schrödinger operators with sparse potentials: Asymptotics of the Fourier transform of the spectral measure, Comm. Math. Phys., 223, 509, 10.1007/s002200100552
Lancaster, 1985
Last, 1996, Quantum dynamics and decomposition of singular continuous spectra, J. Funct. Anal., 142, 406, 10.1006/jfan.1996.0155
Last, 1999, Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators, Invent. Math., 135, 329, 10.1007/s002220050288
Marchetti, 2007, Spectral transition in a sparse model and a class of nonlinear dynamical systems, Nonlinearity, 20, 765, 10.1088/0951-7715/20/3/010
Pearson, 1978, Singular continuous measures in the scattering theory, Comm. Math. Phys., 60, 13, 10.1007/BF01609472
Pearson, 1993, Value distribution and spectral analysis of differential operators, J. Phys. A, 26, 4067, 10.1088/0305-4470/26/16/022
Reed, 1995
Rogers, 1959, The analysis of additive set functions in Euclidean space, Acta Math., 101, 273, 10.1007/BF02559557
Saks, 1937
Simon, 1996, Operators with singular continuous spectrum, V. Sparse potentials, Proc. Amer. Math. Soc., 124, 2073, 10.1090/S0002-9939-96-03465-X
Teschl, 2000
Zlatoš, 2004, Sparse potentials with fractional Hausdorff dimension, J. Funct. Anal., 207, 216, 10.1016/S0022-1236(03)00180-0