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Volumn 357, Issue 2, 2005, Pages 571-615

Analysis on products of fractals

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EID: 13844299233     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03685-2     Document Type: Article
Times cited : (42)

References (33)
  • 1
    • 0035839352 scopus 로고    scopus 로고
    • Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients
    • [B] . MR 1846743 (2002i:35002)
    • [B] G. Barbatis, Explicit estimates on the fundamental solution of higher-order parabolic equations with measurable coefficients, J. Diff. Eq. 174 (2001), 442-463. MR 1846743 (2002i:35002)
    • (2001) J. Diff. Eq. , vol.174 , pp. 442-463
    • Barbatis, G.1
  • 2
    • 0000115419 scopus 로고    scopus 로고
    • Sharp bounds on heat kernels of higher order uniform operators
    • [BD] . MR 1417193 (97k:35105)
    • [BD] G. Barbatis and E. B. Davies, Sharp bounds on heat kernels of higher order uniform operators, J. Operator Theory 36 (1996), 179-198. MR 1417193 (97k:35105)
    • (1996) J. Operator Theory , vol.36 , pp. 179-198
    • Barbatis, G.1    Davies, E.B.2
  • 3
    • 0002163683 scopus 로고    scopus 로고
    • Diffusion on fractals
    • [Ba] Springer, MR 1668115 (2000a:60148)
    • [Ba] M. Barlow, Diffusion on fractals, Lecture Notes Math., vol. 1690, Springer, 1998. MR 1668115 (2000a:60148)
    • (1998) Lecture Notes Math. , vol.1690
    • Barlow, M.1
  • 4
    • 0000835875 scopus 로고
    • Brownian motion on the Sierpinski gasket
    • [BP] . MR 0966175 (89g:60241)
    • [BP] M. Barlow and E. Perkins, Brownian motion on the Sierpinski gasket, Probab. Theory Related Fields 79 (1988), 543-623. MR 0966175 (89g:60241)
    • (1988) Probab. Theory Related Fields , vol.79 , pp. 543-623
    • Barlow, M.1    Perkins, E.2
  • 5
    • 0001511211 scopus 로고    scopus 로고
    • What is not in the domain of the Laplacian on Sierpinski gasket type fractals
    • [BST] . MR 1707752 (2001e:31016)
    • [BST] O. Ben-Bassat, R. Strichartz and A. Teplyaev, What is not in the domain of the Laplacian on Sierpinski gasket type fractals, J. of Functional Analysis 166 (1999), 197-217. MR 1707752 (2001e:31016)
    • (1999) J. of Functional Analysis , vol.166 , pp. 197-217
    • Ben-Bassat, O.1    Strichartz, R.2    Teplyaev, A.3
  • 7
    • 0002902660 scopus 로고
    • Potential theory on the infinite dimensional torus
    • [Be] . MR 0402093 (53:5915)
    • [Be] C. Berg, Potential theory on the infinite dimensional torus, Inv. Math. 32 (1976), 49-100. MR 0402093 (53:5915)
    • (1976) Inv. Math. , vol.32 , pp. 49-100
    • Berg, C.1
  • 9
    • 0346901926 scopus 로고    scopus 로고
    • Off-diagonal heat kernel lower bounds without Poincaré
    • [C] . MR 2010012
    • [C] T. Coulhon, Off-diagonal heat kernel lower bounds without Poincaré, J. London Math. Soc. (2) 68 (2003), 795-816. MR 2010012
    • (2003) J. London Math. Soc. (2) , vol.68 , pp. 795-816
    • Coulhon, T.1
  • 11
    • 0347917936 scopus 로고    scopus 로고
    • Fractal differential equations on the Sierpinski gasket
    • [DSV] . MR 1683211 (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 1683211 (2000k:31016)
    • (1999) J. Fourier Anal. Appl. , vol.5 , pp. 203-284
    • Dalrymple, K.1    Strichartz, R.2    Vinson, J.3
  • 12
    • 0037147379 scopus 로고    scopus 로고
    • Plancherel type estimates and sharp spectral multipliers
    • [DOS] . MR 1943098 (2003k:43012)
    • [DOS] X. T. Duong, E. M. Ouhabaz and A. Sikora, Plancherel type estimates and sharp spectral multipliers, J. Funct. Anal. 196 (2002), 443-485. MR 1943098 (2003k:43012)
    • (2002) J. Funct. Anal. , vol.196 , pp. 443-485
    • Duong, X.T.1    Ouhabaz, E.M.2    Sikora, A.3
  • 13
    • 0002832308 scopus 로고
    • On a spectral analysis for the Sierpinski gasket
    • [FS] . MR 1245223 (95b:31009)
    • [FS] M. Fukushima and T. Shima, On a spectral analysis for the Sierpinski gasket, Potential Anal. 1 (1992), 1-35. MR 1245223 (95b:31009)
    • (1992) Potential Anal. , vol.1 , pp. 1-35
    • Fukushima, M.1    Shima, T.2
  • 14
    • 0037407173 scopus 로고    scopus 로고
    • Heat kernels on metric measure spaces and an application to semilinear elliptic equations
    • [GHL] . MR 1953538 (2003j:60103)
    • [GHL] A. Grigor'yan, Jiaxin Hu and Ka-Sing Lau, Heat kernels on metric measure spaces and an application to semilinear elliptic equations, Trans. Amer. Math. Soc. 255 (2003), 2065-2095. MR 1953538 (2003j:60103)
    • (2003) Trans. Amer. Math. Soc. , vol.255 , pp. 2065-2095
    • Grigor'yan, A.1    Hu, J.2    Lau, K.-S.3
  • 15
    • 0001569543 scopus 로고    scopus 로고
    • Transition density estimates for diffusion processes on post critically finite self-similar fractals
    • [HK] . MR 1665249 (99m:60118)
    • [HK] B. Hambly and T. Kumagai, Transition density estimates for diffusion processes on post critically finite self-similar fractals, Proc. London Math. Soc. 78 (3) (1999), 431-458. MR 1665249 (99m:60118)
    • (1999) Proc. London Math. Soc. , vol.78 , Issue.3 , pp. 431-458
    • Hambly, B.1    Kumagai, T.2
  • 16
    • 0000468986 scopus 로고
    • Dirichlet forms on fractals: Poincaré constant and resistance
    • [KZ] . MR 1176724 (94e:60069)
    • [KZ] S. Kasuoka and X. Y. Zhou, Dirichlet forms on fractals: Poincaré constant and resistance, Probab. Theory Related Fields 93 (1992), 169-196. MR 1176724 (94e:60069)
    • (1992) Probab. Theory Related Fields , vol.93 , pp. 169-196
    • Kasuoka, S.1    Zhou, X.Y.2
  • 17
    • 77951516336 scopus 로고
    • A harmonic calculus on the Sierpinski spaces
    • [Ki1] . MR 1001286 (91g:31005)
    • [Ki1] J. Kigami, A harmonic calculus on the Sierpinski spaces, Japan J. Appl. Math. 8 (1989), 259-290. MR 1001286 (91g:31005)
    • (1989) Japan J. Appl. Math. , vol.8 , pp. 259-290
    • Kigami, J.1
  • 18
    • 84924341601 scopus 로고
    • Harmonic calculus on p.c.f. self-similar sets
    • [K2] . MR 1076617 (93d:39008)
    • [K2] J. Kigami, Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc. 335 (1993), 721-755. MR 1076617 (93d:39008)
    • (1993) Trans. Amer. Math. Soc. , vol.335 , pp. 721-755
    • Kigami, J.1
  • 19
    • 0004075170 scopus 로고    scopus 로고
    • [Ki3] Cambridge University Press, New York . MR 1840042 (2002c:28015)
    • [Ki3] J. Kigami, Analysis on Fractals, Cambridge University Press, New York, 2001. MR 1840042 (2002c:28015)
    • (2001) Analysis on Fractals
    • Kigami, J.1
  • 20
    • 0344118760 scopus 로고    scopus 로고
    • Harmonic analysis for resistance forms
    • [Ki4] . MR 2017320
    • [Ki4] J. Kigami, Harmonic analysis for resistance forms, J. Funct. Anal. 204 (2003), 399-444. MR 2017320
    • (2003) J. Funct. Anal. , vol.204 , pp. 399-444
    • Kigami, J.1
  • 21
    • 21444443520 scopus 로고    scopus 로고
    • Renormalization contracts on nested fractals
    • [M] . MR 1420562 (98b:31007)
    • [M] V. Metz, Renormalization contracts on nested fractals, J. Reine Angew. Math. 480 (1996), 161-175. MR 1420562 (98b:31007)
    • (1996) J. Reine Angew. Math. , vol.480 , pp. 161-175
    • Metz, V.1
  • 23
    • 0013533249 scopus 로고    scopus 로고
    • Convergence and uniqueness problems for Dirichlet forms on fractals
    • [P] . MR 1769995 (2001i:31016)
    • [P] R. Peirone, Convergence and uniqueness problems for Dirichlet forms on fractals, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 3 (2000), 431-460. MR 1769995 (2001i:31016)
    • (2000) Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) , vol.3 , pp. 431-460
    • Peirone, R.1
  • 24
    • 0031536927 scopus 로고    scopus 로고
    • Existence and uniqueness of diffusions on finitely ramified self-similar fractals
    • [Sa] . MR 1474807 (98h:60118)
    • [Sa] C. Sabot, Existence and uniqueness of diffusions on finitely ramified self-similar fractals, Ann. Sci. Écoel Norm. Sup (4) 30 (1997), 605-673. MR 1474807 (98h:60118)
    • (1997) Ann. Sci. Écoel Norm. Sup (4) , vol.30 , pp. 605-673
    • Sabot, C.1
  • 25
  • 26
    • 13844265102 scopus 로고
    • On bounds for the Dirichlet integrals
    • [SB] . MR 0076886 (17:959d)
    • [SB] L. N. Slobodeckii and V. M. Babic, On bounds for the Dirichlet integrals (Russian), Doklady Akad. Nauk. S.S.S.R. 106 (1956), 604-606. MR 0076886 (17:959d)
    • (1956) Doklady Akad. Nauk. S.S.S.R. , vol.106 , pp. 604-606
    • Slobodeckii, L.N.1    Babic, V.M.2
  • 27
    • 0001402085 scopus 로고
    • Multipliers on fractional Sobolev spaces
    • [S1] . MR 0215084 (35:5927)
    • [S1] R. Strichartz, Multipliers on fractional Sobolev spaces, J. Math. Mech. 16 (1967), 1031-1060. MR 0215084 (35:5927)
    • (1967) J. Math. Mech. , vol.16 , pp. 1031-1060
    • Strichartz, R.1
  • 28
    • 0033145310 scopus 로고    scopus 로고
    • Some properties of Laplacians on fractals
    • [S2] . MR 1695571 (2000f:35032)
    • [S2] R. Strichartz, Some properties of Laplacians on fractals, J. Funct. Anal. 164 (1999), 181-208. MR 1695571 (2000f:35032)
    • (1999) J. Funct. Anal. , vol.164 , pp. 181-208
    • Strichartz, R.1
  • 29
    • 0000722104 scopus 로고    scopus 로고
    • Analysis on fractals
    • [S3] . MR 1715511 (2000i:58035)
    • [S3] R. Strichartz, Analysis on fractals, Notices Amer. Math. Soc. 46 (1999), 1199-1208. MR 1715511 (2000i:58035)
    • (1999) Notices Amer. Math. Soc. , vol.46 , pp. 1199-1208
    • Strichartz, R.1
  • 30
    • 0038404094 scopus 로고    scopus 로고
    • The Laplacian on the Sierpinski gasket via the method of averages
    • [S4] . MR 1867899 (2003f:35056)
    • [S4] R. Strichartz, The Laplacian on the Sierpinski gasket via the method of averages, Pac. J. Math. 201 (2001), 241-256. MR 1867899 (2003f:35056)
    • (2001) Pac. J. Math. , vol.201 , pp. 241-256
    • Strichartz, R.1
  • 31
    • 0037455846 scopus 로고    scopus 로고
    • Function spaces on fractals
    • [S5]. MR 1962353 (2003m:46058)
    • [S5] R. Strichartz, Function spaces on fractals, J. Funct. Anal. 198 (2003), 43-83. MR 1962353 (2003m:46058)
    • (2003) J. Funct. Anal. , vol.198 , pp. 43-83
    • Strichartz, R.1
  • 32
    • 0242350504 scopus 로고    scopus 로고
    • Fractafolds based on the Sierpinski gasket and their spectra
    • [S6] . MR 1990573 (2004b:28013)
    • [S6] R. Strichartz, Fractafolds based on the Sierpinski gasket and their spectra, Trans. Amer. Math. Soc. 355 (2003), 4019-4043. MR 1990573 (2004b:28013)
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 4019-4043
    • Strichartz, R.1
  • 33


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