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Volumn 355, Issue 10, 2003, Pages 4019-4043

Fractafolds based on the Sierpinski gasket and their spectra

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EID: 0242350504     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-03-03171-4     Document Type: Article
Times cited : (83)

References (25)
  • 1
    • 0242333531 scopus 로고
    • Topological spaces admitting a unique fractal structure
    • [BR]. MR 94c:28009
    • [BR] C. Bandt and T. Retta, Topological spaces admitting a unique fractal structure, Fund. Math. 141 (1992), 257-268.' MR 94c:28009
    • (1992) Fund. Math. , vol.141 , pp. 257-268
    • Bandt, C.1    Retta, T.2
  • 2
    • 0002163683 scopus 로고    scopus 로고
    • Diffusion on fractals
    • [B]. MR 2000a:60148
    • [B] M. Barlow, Diffusion on fractals, Lecture Notes Math., vol.1690 (1998). MR 2000a:60148
    • (1998) Lecture Notes Math. , vol.1690
    • Barlow, M.1
  • 3
    • 0001352912 scopus 로고    scopus 로고
    • Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets
    • [BK]. MR 99b:35162
    • [BK] M. Barlow and J. Kigami, Localized eigenfunctions of the Laplacian on p.c.f. self-similar sets, J. London Math. Soc. 56 (1997), 320-332. MR 99b:35162
    • (1997) J. London Math. Soc. , vol.56 , pp. 320-332
    • Barlow, M.1    Kigami, J.2
  • 4
    • 0000835875 scopus 로고
    • Brownian motion on the Sierpinski gasket
    • [BP]. MR 89g:60241
    • [BP] M. Barlow and E. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Related Fields 79 (1988), 543-623. MR 89g:60241
    • (1988) Probab. Theory Related Fields , vol.79 , pp. 543-623
    • Barlow, M.1    Perkins, E.2
  • 5
    • 0037618811 scopus 로고    scopus 로고
    • The Sunada method
    • [Br1]. MR 2000g:58049
    • [Br1] R. Brooks, The Sunada method, Contemp. Math. 231 (1999), 25-35. MR 2000g:58049
    • (1999) Contemp. Math. , vol.231 , pp. 25-35
    • Brooks, R.1
  • 6
    • 0033449259 scopus 로고    scopus 로고
    • Non-Sunada graphs
    • [Br2]. MR 2000i:58062
    • [Br2] R. Brooks, Non-Sunada graphs, Ann. Inst. Fourier, Grenoble 49 (1999), 707-725. MR 2000i:58062
    • (1999) Ann. Inst. Fourier, Grenoble , vol.49 , pp. 707-725
    • Brooks, R.1
  • 7
    • 0242301980 scopus 로고    scopus 로고
    • [Br3], personal communication
    • [Br3] R. Brooks, personal communication.
    • Brooks, R.1
  • 8
    • 0242270255 scopus 로고
    • Cayley graphs and planar isospectral domains
    • [Bu]. MR 90a:58177
    • [Bu] P. Buser, Cayley graphs and planar isospectral domains, Springer Lecture Notes Math. 1339 (1988), 64-77. MR 90a:58177
    • (1988) Springer Lecture Notes Math. , vol.1339 , pp. 64-77
    • Buser, P.1
  • 9
    • 0347917936 scopus 로고    scopus 로고
    • Fractal differential equations on the Sierpinski gasket
    • [DSV]. MR 2000k:31016
    • [DSV] K. Dalrymple, R. Strichartz and J. Vinson, Fractal differential equations on the Sierpinski gasket, J. Fourier Anal. Appl. 5 (1999), 203-284. MR 2000k:31016
    • (1999) J. Fourier Anal. Appl. , vol.5 , pp. 203-284
    • Dalrymple, K.1    Strichartz, R.2    Vinson, J.3
  • 10
    • 0242301982 scopus 로고
    • Simple plane images of the Sierpinski triangular curve are nowhere dense
    • [DM]. MR 92e:54039
    • [DM] W. Debski and J. Mioduszewski, Simple plane images of the Sierpinski triangular curve are nowhere dense, Colloq. Math. 59 (1990), 125-140. MR 92e:54039
    • (1990) Colloq. Math. , vol.59 , pp. 125-140
    • Debski, W.1    Mioduszewski, J.2
  • 12
    • 0003350935 scopus 로고
    • Harmonic analysis and representation theory for groups acting on homogeneous trees
    • [F-TN]. MR 93f:22004
    • [F-TN] A. Figa-Talamanca and C. Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees, London Math. Soc. Lecture Note Series 182 (1991). MR 93f:22004
    • (1991) London Math. Soc. Lecture Note Series , vol.182
    • Figa-Talamanca, A.1    Nebbia, C.2
  • 13
    • 0002832308 scopus 로고
    • On a spectral analysis for the Sierpinski gasket
    • [FS]. MR 95b:31009
    • [FS] M. Fukushima and T. Shima, On a spectral analysis for the Sierpinski gasket, Potential Anal. 1 (1992), 1-35. MR 95b:31009
    • (1992) Potential Anal. , vol.1 , pp. 1-35
    • Fukushima, M.1    Shima, T.2
  • 14
    • 0035537148 scopus 로고    scopus 로고
    • The finite element method on the Sierpinski gasket
    • [GRS]. MR 20021:28010
    • [GRS] M. Gibbons, A. Raj and R. Strichartz, The finite element method on the Sierpinski gasket, Constructive Approx. 17 (2001), 561-588. MR 20021:28010
    • (2001) Constructive Approx. , vol.17 , pp. 561-588
    • Gibbons, M.1    Raj, A.2    Strichartz, R.3
  • 15
    • 0004075170 scopus 로고    scopus 로고
    • [Ki1], Cambridge University Press. MR 2002c:28015
    • [Ki1] J. Kigami, Analysis on Fractals, Cambridge University Press, 2001. MR 2002c:28015
    • (2001) Analysis on Fractals
    • Kigami, J.1
  • 16
    • 0242333532 scopus 로고    scopus 로고
    • Harmonic analysis for resistance forms
    • [Ki2], to appear
    • [Ki2] J. Kigami, Harmonic analysis for resistance forms, J. Functional Anal., to appear.
    • J. Functional Anal.
    • Kigami, J.1
  • 19
    • 0031536927 scopus 로고    scopus 로고
    • Existence and uniqueness of diffusions on finitely ramified self-similar fractals
    • [Sa]. MR 98h:60118
    • eme série 30 (1997), 605-673. MR 98h:60118
    • (1997) eme Série , vol.30 , pp. 605-673
    • Sabot, C.1
  • 20
    • 0000381989 scopus 로고
    • On eigenvalue problems for the random walks on the Sierpinski pre-gaskets
    • [Sh1]. MR 92g:60094
    • [Sh1] T. Shima, On eigenvalue problems for the random walks on the Sierpinski pre-gaskets, Japan J. Indust. Appl. Math. 8 (1991), 127-141. MR 92g:60094
    • (1991) Japan J. Indust. Appl. Math. , vol.8 , pp. 127-141
    • Shima, T.1
  • 21
    • 0002230189 scopus 로고    scopus 로고
    • On eigenvalue problems for Laplacians on p.c.f. self-similar sets
    • [Sh2]. MR 97f:28028
    • [Sh2] T. Shima, On eigenvalue problems for Laplacians on p.c.f. self-similar sets, Japan J. Indust. Appl. Math. 13 (1996), 1-23. MR 97f:28028
    • (1996) Japan J. Indust. Appl. Math. , vol.13 , pp. 1-23
    • Shima, T.1
  • 22
    • 22844454199 scopus 로고    scopus 로고
    • The spectrum of infinite regular line graphs
    • [Shi]. MR 2001f:05092
    • [Shi] T. Shirai, The spectrum of infinite regular line graphs, Trans. Amer. Math. Soc. 352 (1999), 115-132. MR 2001f:05092
    • (1999) Trans. Amer. Math. Soc. , vol.352 , pp. 115-132
    • Shirai, T.1
  • 23
    • 0032393182 scopus 로고    scopus 로고
    • Fractals in the large
    • [S1]. MR 99f:28015
    • [S1] R. Strichartz, Fractals in the large, Can. J. Math. 50 (1998), 638-657. MR 99f:28015
    • (1998) Can. J. Math. , vol.50 , pp. 638-657
    • Strichartz, R.1
  • 25
    • 0000604124 scopus 로고
    • Spectral analysis on infinite Sierpinski gaskets
    • [T]. MR 99j:35153
    • [T] A. Teplyaev, Spectral analysis on infinite Sierpinski gaskets, J. Functional Anal. 159 (1989), 537-567. MR 99j:35153
    • (1989) J. Functional Anal. , vol.159 , pp. 537-567
    • Teplyaev, A.1


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