메뉴 건너뛰기




Volumn 164, Issue 2, 1999, Pages 181-208

Some properties of Laplacians on fractals

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0033145310     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.1999.3400     Document Type: Article
Times cited : (57)

References (26)
  • 1
    • 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. (2). 56:1997;320-332.
    • (1997) J. London Math. Soc. (2) , vol.56 , pp. 320-332
    • Barlow, M.T.1    Kigami, J.2
  • 3
    • 0001511211 scopus 로고    scopus 로고
    • What is not in the domain of the Laplacian on a Sierpinski gasket type fractal
    • O. Ben-Bassat, R. Strichartz, A. Teplyaev, What is not in the domain of the Laplacian on a Sierpinski gasket type fractal, J. Funct. Anal.
    • J. Funct. Anal.
    • Ben-Bassat, O.1    Strichartz, R.2    Teplyaev, A.3
  • 4
    • 49549162581 scopus 로고
    • Essential self-adjointness of powers of generators of hyperbolic equations
    • Chernoff P. Essential self-adjointness of powers of generators of hyperbolic equations. J. Funct. Anal. 12:1973;401-414.
    • (1973) J. Funct. Anal. , vol.12 , pp. 401-414
    • Chernoff, P.1
  • 6
    • 0002832308 scopus 로고
    • On a spectral analysis for the Sierpinski gasket
    • Fukushima M., Shima T. On a spectral analysis for the Sierpinski gasket. Potential Anal. 1:1992;1-35.
    • (1992) Potential Anal. , vol.1 , pp. 1-35
    • Fukushima, M.1    Shima, T.2
  • 7
    • 84968508586 scopus 로고
    • Noncommuting random products
    • Furstenberg H. Noncommuting random products. Trans. Amer. Math. Soc. 108:1963;377-428.
    • (1963) Trans. Amer. Math. Soc. , vol.108 , pp. 377-428
    • Furstenberg, H.1
  • 9
    • 0001582569 scopus 로고
    • Random walks and diffusions on fractals
    • Percolation Theory and Ergodic Theory of Infinite Particle Systems. H. Kesten. New York: Springer
    • Goldstein S. Random walks and diffusions on fractals. Kesten H., Percolation Theory and Ergodic Theory of Infinite Particle Systems. IMA Math. Appl. 8:1987;121-129 Springer, New York.
    • (1987) IMA Math. Appl. , vol.8 , pp. 121-129
    • Goldstein, S.1
  • 10
    • 77951516336 scopus 로고
    • A harmonic calculus on the Sierpinski spaces
    • Kigami J. A harmonic calculus on the Sierpinski spaces. Jpn. J. Appl. Math. 6:1989;259-290.
    • (1989) Jpn. J. Appl. Math. , vol.6 , pp. 259-290
    • Kigami, J.1
  • 11
    • 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
  • 12
    • 0000620294 scopus 로고
    • Laplacians on self-similar sets and their spectral distributions
    • Progress in Probability. Basel: Birkhäuser. p. 221-238
    • Kigami J. Laplacians on self-similar sets and their spectral distributions. Fractal Geometry and Stochastics, Finsterbergen, 1994. Progress in Probability. 37:1995;Birkhäuser, Basel. p. 221-238.
    • (1995) Fractal Geometry and Stochastics, Finsterbergen, 1994 , vol.37
    • Kigami, J.1
  • 13
    • 84973971662 scopus 로고
    • Effective resistances for harmonic structures on p.c.f. self-similar sets
    • Kigami J. Effective resistances for harmonic structures on p.c.f. self-similar sets. Math. Proc. Cambridge Philos. Soc. 115:1994;291-303.
    • (1994) Math. Proc. Cambridge Philos. Soc. , vol.115 , pp. 291-303
    • Kigami, J.1
  • 14
    • 0000406745 scopus 로고    scopus 로고
    • Distributions of localized eigenvalues of Laplacian on p.c.f. self-similar sets
    • 198
    • Kigami J. Distributions of localized eigenvalues of Laplacian on p.c.f. self-similar sets. J. Funct. Anal. 156:198;170-198.
    • J. Funct. Anal. , vol.156 , pp. 170-198
    • Kigami, J.1
  • 16
    • 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. Commun. Math. Phys. 158:1993;93-125.
    • (1993) Commun. Math. Phys. , vol.158 , pp. 93-125
    • Kigami, J.1    Lapidus, M.L.2
  • 18
    • 85008054100 scopus 로고
    • Dirichlet forms on fractals and products of random matrices
    • Kusuoka S. Dirichlet forms on fractals and products of random matrices. Publ. RIMS. 25:1989;659-680.
    • (1989) Publ. RIMS , vol.25 , pp. 659-680
    • Kusuoka, S.1
  • 19
    • 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. Topolog. Methods in Nonlinear Anal. 4:1994;137-195.
    • (1994) Topolog. Methods in Nonlinear Anal. , vol.4 , pp. 137-195
    • Lapidus, M.L.1
  • 20
    • 0000311503 scopus 로고
    • Brownian motion on nested fractals
    • Lindstrom T. Brownian motion on nested fractals. Mem. Amer. Math. Soc. 420:1989.
    • (1989) Mem. Amer. Math. Soc. , vol.420
    • Lindstrom, T.1
  • 21
    • 0000749451 scopus 로고
    • Dirichlet forms and self-similarity
    • AMS/IP Studies in Advanced Math. Providence: American Math. Society. p. 117-155
    • Mosco U. Dirichlet forms and self-similarity. New Directions in Dirichlet Forms. AMS/IP Studies in Advanced Math. 8:1988;American Math. Society, Providence. p. 117-155.
    • (1988) New Directions in Dirichlet Forms , vol.8
    • Mosco, U.1
  • 23
    • 48749149923 scopus 로고
    • Analysis of the Laplacian on a complete Riemannian manifold
    • Strichartz R. Analysis of the Laplacian on a complete Riemannian manifold. J. Funct. Anal. 52:1983;48-79.
    • (1983) J. Funct. Anal. , vol.52 , pp. 48-79
    • Strichartz, R.1
  • 24
    • 0032393182 scopus 로고    scopus 로고
    • Fractals in the large
    • Strichartz R. Fractals in the large. Can. J. Math. 50:1998;638-657.
    • (1998) Can. J. Math. , vol.50 , pp. 638-657
    • Strichartz, R.1
  • 26
    • 0000604124 scopus 로고    scopus 로고
    • Spectral analysis on infinite Sierpinski gaskets
    • Teplyaev A. Spectral analysis on infinite Sierpinski gaskets. J. Funct. Anal. 159:1998;537-567.
    • (1998) J. Funct. Anal. , vol.159 , pp. 537-567
    • Teplyaev, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.