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Volumn 159, Issue 2, 1998, Pages 537-567

Spectral Analysis on Infinite Sierpiński Gaskets

Author keywords

Fractal graphs; Fractals; Laplacian; Localization; Pure point spectrum

Indexed keywords


EID: 0000604124     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1998.3297     Document Type: Article
Times cited : (134)

References (37)
  • 1
    • 0011379512 scopus 로고
    • Some properties of the spectrum of the Sierpiński gasket in a magnetic field
    • Alexander S. Some properties of the spectrum of the Sierpiński gasket in a magnetic field. Phys. Rev. B. 29:1984;5504-5508.
    • (1984) Phys. Rev. B , vol.29 , pp. 5504-5508
    • Alexander, S.1
  • 2
    • 0038962257 scopus 로고
    • Harmonic analysis on fractal spaces
    • p. 345-368
    • Barlow M. T. Harmonic analysis on fractal spaces. Séminaire Bourbaki. 1992;. p. 345-368.
    • (1992) Séminaire Bourbaki
    • Barlow, M.T.1
  • 3
    • 0001352912 scopus 로고    scopus 로고
    • Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets
    • Barlow M. T., Kigami J. Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets. J. London Math. Soc. 56:1997;320-332.
    • (1997) J. London Math. Soc. , vol.56 , pp. 320-332
    • Barlow, M.T.1    Kigami, J.2
  • 8
    • 21844506818 scopus 로고
    • Operators with singular continuous spectrum. II. Rank one operators
    • Del Rio R., Makarov N., Simon B. Operators with singular continuous spectrum. II. Rank one operators. Comm. Math. Phys. 165:1994;59-67.
    • (1994) Comm. Math. Phys. , vol.165 , pp. 59-67
    • Del Rio, R.1    Makarov, N.2    Simon, B.3
  • 10
    • 0002832308 scopus 로고
    • On a spectral analysis for the Sierpiński gasket
    • Fukushima M., Shima T. On a spectral analysis for the Sierpiński gasket. Potential Anal. 1:1992;1-35.
    • (1992) Potential Anal. , vol.1 , pp. 1-35
    • Fukushima, M.1    Shima, T.2
  • 13
    • 77951516336 scopus 로고
    • A harmonic calculus on the Sierpinski spaces
    • Kigami J. A harmonic calculus on the Sierpinski spaces. Japan J. Appl. Math. 6:1989;259-290.
    • (1989) Japan J. Appl. Math. , vol.6 , pp. 259-290
    • Kigami, J.1
  • 14
    • 84924341601 scopus 로고
    • Harmonic calculus on p.c.f. self-similar sets
    • Kigami J. Harmonic calculus on p.c.f. self-similar sets. Trans. Amer. Math. Soc. 335:1993;721-755.
    • (1993) Trans. Amer. Math. Soc. , vol.335 , pp. 721-755
    • Kigami, J.1
  • 17
    • 21344480546 scopus 로고
    • Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals
    • Kigami J., Lapidus M. L. Weyl's problem for the spectral distribution of Laplacians on p.c.f. self-similar fractals. Comm. Math. Phys. 158:1993;93-125.
    • (1993) Comm. Math. Phys. , vol.158 , pp. 93-125
    • Kigami, J.1    Lapidus, M.L.2
  • 19
    • 85008054100 scopus 로고
    • Dirichlet forms on fractals and products of random matrices
    • Kusuoka S. Dirichlet forms on fractals and products of random matrices. Publ. Res. Inst. Math. Sci. 25:1989;659-680.
    • (1989) Publ. Res. Inst. Math. Sci. , vol.25 , pp. 659-680
    • Kusuoka, S.1
  • 20
    • 0000468986 scopus 로고
    • Dirichlet forms on fractals: Poincare constant and resistance
    • Kusuoka S., Yin Z. X. Dirichlet forms on fractals: Poincare constant and resistance. Probab. Theory Related Fields. 93:1992;169-196.
    • (1992) Probab. Theory Related Fields , vol.93 , pp. 169-196
    • Kusuoka, S.1    Yin, Z.X.2
  • 21
    • 0001313307 scopus 로고
    • Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions
    • Lapidus M. L. Analysis on fractals, Laplacians on self-similar sets, noncommutative geometry and spectral dimensions. Topol. Methods Nonlinear Anal. 4:1994;137-195.
    • (1994) Topol. Methods Nonlinear Anal. , vol.4 , pp. 137-195
    • Lapidus, M.L.1
  • 22
  • 23
    • 3543013147 scopus 로고
    • Spectral theory of the differential Laplacian on the modified Koch curve
    • Providence: Am. Math. Soc. p. 193-224
    • Malozemov L. Spectral theory of the differential Laplacian on the modified Koch curve. Geometry of the Spectrum (Seattle, WA, 1993). Contemp. Math. 173:1994;Am. Math. Soc. Providence. p. 193-224.
    • (1994) Geometry of the Spectrum (Seattle, WA, 1993) Contemp. Math. , vol.173
    • Malozemov, L.1
  • 24
    • 0037571676 scopus 로고
    • Pure point spectrum of the Laplacians on fractal graphs
    • Malozemov L., Teplyaev A. Pure point spectrum of the Laplacians on fractal graphs. J. Funct. Anal. 129:1994;390-405.
    • (1994) J. Funct. Anal. , vol.129 , pp. 390-405
    • Malozemov, L.1    Teplyaev, A.2
  • 26
    • 0021372307 scopus 로고
    • Spectrum of harmonic excitations on fractals
    • Rammal R. Spectrum of harmonic excitations on fractals. J. Physique. 45:1984;191-206.
    • (1984) J. Physique , vol.45 , pp. 191-206
    • Rammal, R.1
  • 27
    • 0020498687 scopus 로고
    • Random walks on fractal structures and percolation clusters
    • Rammal R., Toulouse G. Random walks on fractal structures and percolation clusters. J. Physique Lett. 44:1983;L13-L22.
    • (1983) J. Physique Lett. , vol.44 , pp. 13-L22
    • Rammal, R.1    Toulouse, G.2
  • 29
    • 0000381989 scopus 로고
    • On eigenvalue problems for the random walks on the Sierpinski pre- gaskets
    • Shima T. On eigenvalue problems for the random walks on the Sierpinski pre- gaskets. Japan J. Indust. Appl. Math. 8:1991;127-141.
    • (1991) Japan J. Indust. Appl. Math. , vol.8 , pp. 127-141
    • Shima, T.1
  • 31
    • 0001592725 scopus 로고
    • Operators with singular continuous spectrum. I. General operators
    • Simon B. Operators with singular continuous spectrum. I. General operators. Ann. of Math. 141:1995;131-145.
    • (1995) Ann. of Math. , vol.141 , pp. 131-145
    • Simon, B.1
  • 32
    • 0030544901 scopus 로고    scopus 로고
    • Operators with singular continuous spectrum. VII. Examples with borderline time decay
    • Simon B. Operators with singular continuous spectrum. VII. Examples with borderline time decay. Comm. Math. Phys. 176:1996;713-722.
    • (1996) Comm. Math. Phys. , vol.176 , pp. 713-722
    • Simon, B.1
  • 33
    • 84990576488 scopus 로고
    • Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians
    • Simon B., Wolff T. Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Comm. Pure Appl. Math. 39:1986;75-90.
    • (1986) Comm. Pure Appl. Math. , vol.39 , pp. 75-90
    • Simon, B.1    Wolff, T.2
  • 34
    • 85088282315 scopus 로고    scopus 로고
    • Isoperimetric estimates on Sierpinski gasket type fractals
    • R. S. Strichartz, Isoperimetric estimates on Sierpinski gasket type fractals, Trans. Amer. Math. Soc.
    • Trans. Amer. Math. Soc.
    • Strichartz, R.S.1
  • 36
    • 1842730303 scopus 로고    scopus 로고
    • Piecewise linear wavelets on Sierpinski gasket type fractals
    • Strichartz R. S. Piecewise linear wavelets on Sierpinski gasket type fractals. J. Fourier. Anal. Appl. 3:1997;387-416.
    • (1997) J. Fourier. Anal. Appl. , vol.3 , pp. 387-416
    • Strichartz, R.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.