메뉴 건너뛰기




Volumn 256, Issue 12, 2009, Pages 3977-3995

Eigenvalue inequalities for Klein-Gordon operators

Author keywords

Cauchy process; Dirac equation; Dirichlet problem; Fractional Laplacian; Klein Gordon equation; Relativistic particle; Riesz means; Semiclassical; Universal bounds; Weyl law

Indexed keywords


EID: 64549133375     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2008.12.008     Document Type: Article
Times cited : (31)

References (43)
  • 1
    • 0036475162 scopus 로고    scopus 로고
    • The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H.C. Yang
    • Spectral and Inverse Spectral Theory. Goa, 2000
    • Ashbaugh M.S. The universal eigenvalue bounds of Payne-Pólya-Weinberger, Hile-Protter, and H.C. Yang. Spectral and Inverse Spectral Theory. Goa, 2000. Proc. Indian Acad. Sci. Math. Sci. vol. 112 (2002) 3-30
    • (2002) Proc. Indian Acad. Sci. Math. Sci. , vol.112 , pp. 3-30
    • Ashbaugh, M.S.1
  • 2
    • 12744260598 scopus 로고    scopus 로고
    • A unified approach to universal inequalities for eigenvalues of elliptic operators
    • Ashbaugh M.S., and Hermi L. A unified approach to universal inequalities for eigenvalues of elliptic operators. Pacific J. Math. 217 (2004) 201-220
    • (2004) Pacific J. Math. , vol.217 , pp. 201-220
    • Ashbaugh, M.S.1    Hermi, L.2
  • 3
    • 0003312088 scopus 로고
    • Isoperimetric Inequalities and Applications
    • Pitman, Boston
    • Bandle C. Isoperimetric Inequalities and Applications. Pitman Monogr. Stud. Math. vol. 7 (1980), Pitman, Boston
    • (1980) Pitman Monogr. Stud. Math. , vol.7
    • Bandle, C.1
  • 4
    • 2942668409 scopus 로고    scopus 로고
    • Eigenvalue gaps for the Cauchy process and a Poincaré inequality
    • Bañuelos R., and Kulczycki T. Eigenvalue gaps for the Cauchy process and a Poincaré inequality. J. Funct. Anal. 211 2 (2004) 355-423
    • (2004) J. Funct. Anal. , vol.211 , Issue.2 , pp. 355-423
    • Bañuelos, R.1    Kulczycki, T.2
  • 5
    • 33645841343 scopus 로고    scopus 로고
    • The Cauchy process and the Steklov problem
    • Bañuelos R., and Kulczycki T. The Cauchy process and the Steklov problem. J. Funct. Anal. 234 (2006) 199-225
    • (2006) J. Funct. Anal. , vol.234 , pp. 199-225
    • Bañuelos, R.1    Kulczycki, T.2
  • 6
    • 0003308484 scopus 로고
    • Spectral Geometry: Direct and Inverse Problems
    • Springer-Verlag, Berlin
    • Bérard P.H. Spectral Geometry: Direct and Inverse Problems. Lecture Notes in Math. vol. 1207 (1986), Springer-Verlag, Berlin
    • (1986) Lecture Notes in Math. , vol.1207
    • Bérard, P.H.1
  • 7
    • 0001146196 scopus 로고
    • Convariant and contravariant symbols of operators
    • (in Russian); English transl. in
    • Berezin F. Convariant and contravariant symbols of operators. Izv. Akad. Nauk SSSR 37 (1972) 1134-1167 (in Russian); English transl. in
    • (1972) Izv. Akad. Nauk SSSR , vol.37 , pp. 1134-1167
    • Berezin, F.1
  • 8
    • 84931493237 scopus 로고
    • Convariant and contravariant symbols of operators
    • Berezin F. Convariant and contravariant symbols of operators. Math. USSR Izv. 6 (1972) 1117-1151
    • (1972) Math. USSR Izv. , vol.6 , pp. 1117-1151
    • Berezin, F.1
  • 11
    • 15244354281 scopus 로고    scopus 로고
    • Estimates on eigenvalues of Laplacian
    • Cheng Q.M., and Yang H.C. Estimates on eigenvalues of Laplacian. Math. Ann. 331 (2005) 445-460
    • (2005) Math. Ann. , vol.331 , pp. 445-460
    • Cheng, Q.M.1    Yang, H.C.2
  • 12
    • 33745633636 scopus 로고    scopus 로고
    • Inequalities for eigenvalues of Laplacian on domains and complex hypersurfaces in complex projective spaces
    • Cheng Q.M., and Yang H.C. Inequalities for eigenvalues of Laplacian on domains and complex hypersurfaces in complex projective spaces. J. Math. Soc. Japan 58 (2006) 545-561
    • (2006) J. Math. Soc. Japan , vol.58 , pp. 545-561
    • Cheng, Q.M.1    Yang, H.C.2
  • 13
    • 33744773463 scopus 로고    scopus 로고
    • Inequalities for eigenvalues of a clamped plate problem
    • Cheng Q.M., and Yang H.C. Inequalities for eigenvalues of a clamped plate problem. Trans. Amer. Math. Soc. 358 (2006) 2625-2635
    • (2006) Trans. Amer. Math. Soc. , vol.358 , pp. 2625-2635
    • Cheng, Q.M.1    Yang, H.C.2
  • 15
    • 68949106024 scopus 로고    scopus 로고
    • Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds
    • in press
    • A. El Soufi, E.M. Harrell II, S. Ilias, Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds, Trans. Amer. Math. Soc., in press
    • Trans. Amer. Math. Soc
    • El Soufi, A.1    Harrell II, E.M.2    Ilias, S.3
  • 18
    • 33947172418 scopus 로고    scopus 로고
    • Commutators, eigenvalue gaps, and mean curvature in the theory of Schrödinger operators
    • Harrell II E.M. Commutators, eigenvalue gaps, and mean curvature in the theory of Schrödinger operators. Comm. Partial Differential Equations 32 (2007) 401-413
    • (2007) Comm. Partial Differential Equations , vol.32 , pp. 401-413
    • Harrell II, E.M.1
  • 19
    • 43049110988 scopus 로고    scopus 로고
    • Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues
    • Harrell II E.M., and Hermi L. Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues. J. Funct. Anal. 254 (2008) 3173-3191
    • (2008) J. Funct. Anal. , vol.254 , pp. 3173-3191
    • Harrell II, E.M.1    Hermi, L.2
  • 20
    • 84862989105 scopus 로고
    • Commutator bounds for eigenvalues, with applications to spectral geometry
    • Harrell II E.M., and Michel P.L. Commutator bounds for eigenvalues, with applications to spectral geometry. Comm. Partial Differential Equations 19 (1994) 2037-2055
    • (1994) Comm. Partial Differential Equations , vol.19 , pp. 2037-2055
    • Harrell II, E.M.1    Michel, P.L.2
  • 21
    • 64549137696 scopus 로고
    • Commutator bounds for eigenvalues, with applications to spectral geometry
    • Erratum
    • Harrell II E.M., and Michel P.L. Commutator bounds for eigenvalues, with applications to spectral geometry. Comm. Partial Differential Equations 20 (1995) 1453 Erratum
    • (1995) Comm. Partial Differential Equations , vol.20 , pp. 1453
    • Harrell II, E.M.1    Michel, P.L.2
  • 22
    • 3142540133 scopus 로고
    • Commutator bounds for eigenvalues of some differential operators
    • Ferreyra G., Goldstein G., and Neubrander F. (Eds), Dekker, New York
    • Harrell II E.M., and Michel P.L. Commutator bounds for eigenvalues of some differential operators. In: Ferreyra G., Goldstein G., and Neubrander F. (Eds). Evolution Equations (1994), Dekker, New York 235-244
    • (1994) Evolution Equations , pp. 235-244
    • Harrell II, E.M.1    Michel, P.L.2
  • 23
    • 21744444664 scopus 로고    scopus 로고
    • On trace identities and universal eigenvalue estimates for some partial differential operators
    • Harrell II E.M., and Stubbe J. On trace identities and universal eigenvalue estimates for some partial differential operators. Trans. Amer. Math. Soc. 349 (1997) 1797-1809
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 1797-1809
    • Harrell II, E.M.1    Stubbe, J.2
  • 25
    • 38749098861 scopus 로고    scopus 로고
    • Extremum Problems for Eigenvalues of Elliptic Operators
    • Birkhäuser
    • Henrot A. Extremum Problems for Eigenvalues of Elliptic Operators. Front. Math. (2006), Birkhäuser
    • (2006) Front. Math.
    • Henrot, A.1
  • 26
    • 0000582072 scopus 로고
    • Inequalities for eigenvalues of the Laplacian
    • Hile G.N., and Protter M.H. Inequalities for eigenvalues of the Laplacian. Indiana Univ. Math. J. 29 (1980) 523-538
    • (1980) Indiana Univ. Math. J. , vol.29 , pp. 523-538
    • Hile, G.N.1    Protter, M.H.2
  • 27
    • 34547327593 scopus 로고    scopus 로고
    • Chiral Gauge theory for graphene
    • Jackiw R., and Pi S.-Y. Chiral Gauge theory for graphene. Phys. Rev. Lett. 98 (2007) 266402
    • (2007) Phys. Rev. Lett. , vol.98 , pp. 266402
    • Jackiw, R.1    Pi, S.-Y.2
  • 28
    • 64549117909 scopus 로고    scopus 로고
    • A. Laptev, T. Weidl, Recent Results on Lieb-Thirring inequalities, Journées Équations aux Dérivées Partielles, La Chapelle sur Erdre, 2000, XX (2002), Univ. Nantes, Nantes, 2000, 14 pp
    • A. Laptev, T. Weidl, Recent Results on Lieb-Thirring inequalities, Journées "Équations aux Dérivées Partielles," La Chapelle sur Erdre, 2000, XX (2002), Univ. Nantes, Nantes, 2000, 14 pp
  • 29
    • 0021976070 scopus 로고
    • Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity
    • Levine H.A., and Protter M.H. Unrestricted lower bounds for eigenvalues for classes of elliptic equations and systems of equations with applications to problems in elasticity. Math. Methods Appl. Sci. 7 (1985) 210-222
    • (1985) Math. Methods Appl. Sci. , vol.7 , pp. 210-222
    • Levine, H.A.1    Protter, M.H.2
  • 30
    • 0037055186 scopus 로고    scopus 로고
    • Commutators, spectral trace identities, and universal estimates for eigenvalues
    • Levitin M., and Parnovski L. Commutators, spectral trace identities, and universal estimates for eigenvalues. J. Funct. Anal. 192 (2002) 425-445
    • (2002) J. Funct. Anal. , vol.192 , pp. 425-445
    • Levitin, M.1    Parnovski, L.2
  • 31
    • 51249182089 scopus 로고
    • Eigenvalue estimates on homogeneous manifolds
    • Li P. Eigenvalue estimates on homogeneous manifolds. Comment. Math. Helv. 55 (1980) 347-363
    • (1980) Comment. Math. Helv. , vol.55 , pp. 347-363
    • Li, P.1
  • 32
    • 0000538029 scopus 로고
    • On the Schrödinger equation and the eigenvalue problem
    • Li P., and Yau S.-T. On the Schrödinger equation and the eigenvalue problem. Comm. Math. Phys. 88 (1983) 309-318
    • (1983) Comm. Math. Phys. , vol.88 , pp. 309-318
    • Li, P.1    Yau, S.-T.2
  • 37
    • 0003232762 scopus 로고    scopus 로고
    • Lévy Processes and Infinitely Divisible Distributions
    • Cambridge University Press, Cambridge
    • Sato K. Lévy Processes and Infinitely Divisible Distributions. Cambridge Stud. Adv. Math. vol. 68 (1999), Cambridge University Press, Cambridge
    • (1999) Cambridge Stud. Adv. Math. , vol.68
    • Sato, K.1
  • 39
    • 36149007340 scopus 로고
    • The band theory of graphite
    • Wallace P.R. The band theory of graphite. Phys. Rev. 71 (1947) 622-634
    • (1947) Phys. Rev. , vol.71 , pp. 622-634
    • Wallace, P.R.1
  • 40
    • 33847342132 scopus 로고    scopus 로고
    • Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds
    • Wang Q., and Xia C. Universal bounds for eigenvalues of the biharmonic operator on Riemannian manifolds. J. Funct. Anal. 245 (2007) 334-352
    • (2007) J. Funct. Anal. , vol.245 , pp. 334-352
    • Wang, Q.1    Xia, C.2
  • 41
    • 34548432536 scopus 로고    scopus 로고
    • Estimate for eigenvalues of Laplacian operator with any order
    • Wu F.E., and Cao L.F. Estimate for eigenvalues of Laplacian operator with any order. Sci. China Ser. A 50 (2007) 1078-1086
    • (2007) Sci. China Ser. A , vol.50 , pp. 1078-1086
    • Wu, F.E.1    Cao, L.F.2
  • 43
    • 0001991729 scopus 로고
    • Eigenvalues of the Laplacian of a compact Riemann surfaces and minimal submanifolds
    • Yang P.C., and Yau S.-T. Eigenvalues of the Laplacian of a compact Riemann surfaces and minimal submanifolds. Ann. Scuola Norm. Sup. Pisa, Cl. Sci. 4 (1980) 55-63
    • (1980) Ann. Scuola Norm. Sup. Pisa, Cl. Sci. , vol.4 , pp. 55-63
    • Yang, P.C.1    Yau, S.-T.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.