메뉴 건너뛰기




Volumn 110, Issue 1, 2001, Pages 1-35

The spectral bound and principal eigenvalues of Schrödinger operators on Riemannian manifolds

(1)  Ouhabaz, El Maati a  

a NONE

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0142256551     PISSN: 00127094     EISSN: None     Source Type: Journal    
DOI: 10.1215/S0012-7094-01-11011-9     Document Type: Article
Times cited : (15)

References (19)
  • 1
    • 84966198483 scopus 로고
    • Principal eigenvalues for indefinite-weight elliptic problems in $\mathbbR∧n$
    • [Al]
    • [Al] W. Allegretto, Principal eigenvalues for indefinite-weight elliptic problems in $\mathbbR∧n$, Proc. Amer. Math. Soc. 116 (1992), 701-706.
    • (1992) Proc. Amer. Math. Soc. , vol.116 , pp. 701-706
    • Allegretto, W.1
  • 2
    • 84972545997 scopus 로고
    • Exponential stability of a diffusion equation with absorption
    • [ABI]
    • [ABI] W. Arendt and C. J. K. Batty, Exponential stability of a diffusion equation with absorption, Differential Integral Equations 6 (1993), 1009-1024.
    • (1993) Differential Integral Equations , vol.6 , pp. 1009-1024
    • Arendt, W.1    Batty, C.J.K.2
  • 3
    • 0031532360 scopus 로고    scopus 로고
    • The spectral function and principal eigenvalues for Schrödinger operators
    • [AB2] _
    • [AB2] _, The spectral function and principal eigenvalues for Schrödinger operators, Potential Anal. 7 (1997), 415-436.
    • (1997) Potential Anal. , vol.7 , pp. 415-436
  • 4
    • 0003255464 scopus 로고
    • Nonlinear Analysis on Manifolds: Monge-Ampère Equations
    • [Au] Springer, New York
    • [Au] T. Aubin, Nonlinear Analysis on Manifolds: Monge-Ampère Equations, Grundlehren Math. Wiss. 252, Springer, New York, 1982.
    • (1982) Grundlehren Math. Wiss. , vol.252
    • Aubin, T.1
  • 5
    • 0000864917 scopus 로고
    • A relation between growth and the spectrum of the Laplacian
    • [Br]
    • [Br] R. Brooks, A relation between growth and the spectrum of the Laplacian, Math. Z. 178 (1981), 501-508.
    • (1981) Math. Z. , vol.178 , pp. 501-508
    • Brooks, R.1
  • 6
    • 84966229474 scopus 로고
    • Principal eigenvalues for problems with indefinite weight function on $\mathbbR∧N$
    • [BCF]
    • [BCF] K. J. Brown, C. Cosner, and J. Fleckinger, Principal eigenvalues for problems with indefinite weight function on $\mathbbR∧N$, Proc. Amer. Math. Soc. 109 (1990), 147-155.
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 147-155
    • Brown, K.J.1    Cosner, C.2    Fleckinger, J.3
  • 8
    • 0000720752 scopus 로고
    • A note on the isoperimetric constant
    • \bibitem [Bu]
    • \bibitem [Bu] Bu P. Buser, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. (4) 15 (1982), 213-230.
    • (1982) Ann. Sci. École Norm. Sup. (4) , vol.15 , pp. 213-230
    • Buser, B.P.1
  • 9
    • 0040348557 scopus 로고    scopus 로고
    • $L∧2$-cohomologie et inégalités de Sobolev
    • [Car]
    • [Car] G. Carron, $L∧2$-cohomologie et inégalités de Sobolev, Math. Ann. 314 (1999), 613-639.
    • (1999) Math. Ann. , vol.314 , pp. 613-639
    • Carron, G.1
  • 10
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • [CGT]
    • [CGT] J. Cheeger, M. Gromov, and M. Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geom. 17 (1982), 15-53.
    • (1982) J. Differential Geom. , vol.17 , pp. 15-53
    • Cheeger, J.1    Gromov, M.2    Taylor, M.3
  • 11
    • 0001691206 scopus 로고
    • Isopérimétrie pour les groupes et les variétés
    • \bibitem [CS]
    • \bibitem [CS] CS T. Coulhon and L. Saloff-Coste, Isopérimétrie pour les groupes et les variétés, Rev. Mat. Iberoamericana 9 (1993), 293-314.
    • (1993) Rev. Mat. Iberoamericana , vol.9 , pp. 293-314
    • Coulhon, C.S.T.1    Saloff-Coste, L.2
  • 12
    • 0039388920 scopus 로고
    • Principal eigenvalues for some periodic-parabolic operators on $\mathbbR∧N$ and related topics
    • \bibitem [Da] Da
    • \bibitem [Da] Da D. Daners, Principal eigenvalues for some periodic-parabolic operators on $\mathbbR∧N$ and related topics, J. Differential Equations 121 (1995), 293-313.
    • (1995) J. Differential Equations , vol.121 , pp. 293-313
    • Daners, D.1
  • 13
    • 0003287060 scopus 로고
    • Heat Kernels and Spectral Theory
    • \bibitem [Dav] Dav Cambridge Univ. Press, Cambridge
    • \bibitem [Dav] Dav E. B. Davies, Heat Kernels and Spectral Theory, Cambridge Tracts in Math. 92, Cambridge Univ. Press, Cambridge, 1989.
    • (1989) Cambridge Tracts in Math. , vol.92
    • Davies, E.B.1
  • 14
    • 0000069050 scopus 로고
    • On the bass note of a Schottky group
    • [Doy]
    • [Doy] P. G. Doyle, On the bass note of a Schottky group, Acta Math. 160 (1988), 249-284.
    • (1988) Acta Math. , vol.160 , pp. 249-284
    • Doyle, P.G.1
  • 15
    • 0030602110 scopus 로고    scopus 로고
    • Semigroup kernels, Poisson bounds, and holomorphic functional calculus
    • \bibitem [DR]
    • \bibitem [DR] DR X. T. Duong and D. W. Robinson, Semigroup kernels, Poisson bounds, and holomorphic functional calculus, J. Funct. Anal. 142 (1996), 89-128.
    • (1996) J. Funct. Anal. , vol.142 , pp. 89-128
    • Duong, X.T.1    Robinson, D.W.2
  • 16
    • 0003523792 scopus 로고
    • Dirichlet Forms and Symmetric Markov Processes
    • \bibitem [FOT] EOT M. Fukushima, Y. Oshima, and M. Takeda, de Gruyter, Berlin
    • \bibitem [FOT] EOT M. Fukushima, Y. \=Oshima, and M. Takeda, Dirichlet Forms and Symmetric Markov Processes, de Gruyter Stud. Math. 19, de Gruyter, Berlin, 1994.
    • (1994) De Gruyter Stud. Math. , vol.19
  • 18
    • 84956248060 scopus 로고
    • Stochastically complete manifolds and summable harmonic functions
    • \bibitem [Gr1]
    • \bibitem [Gr1] Gr1 A. A. Grigor'yan, Stochastically complete manifolds and summable harmonic functions, Math. USSR-Izv. 33 (1989), 425-432.
    • (1989) Math. USSR-Izv. , vol.33 , pp. 425-432
    • Grigor'Yan, G.A.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.