메뉴 건너뛰기




Volumn 24, Issue 3, 2012, Pages

Bounds for the eigenvalues of the fractional laplacian

Author keywords

Eigenvalue; fractional Laplacian; P lya's inequality; transform

Indexed keywords


EID: 84859130342     PISSN: 0129055X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0129055X12500031     Document Type: Review
Times cited : (9)

References (23)
  • 1
    • 0000545486 scopus 로고
    • On semi-classical bounds for eigenvalues of Schrödinger operators
    • M. Aizenman and E. H. Lieb, On semi-classical bounds for eigenvalues of Schrödinger operators, Phys. Lett. A 66 (1978) 427-429.
    • (1978) Phys. Lett. A , vol.66 , pp. 427-429
    • Aizenman, M.1    Lieb, E.H.2
  • 2
    • 2942668409 scopus 로고    scopus 로고
    • The Cauchy process and the Steklov problem
    • DOI 10.1016/j.jfa.2004.02.005
    • R. Banuelos and T. Kulczycki, The Cauchy process and the Steklov problem, J. Funct. Anal. 211(2) (2004) 355-423. (Pubitemid 38773471)
    • (2004) Journal of Functional Analysis , vol.211 , Issue.2 , pp. 355-423
    • Banuelos, R.1    Kulczycki, T.2
  • 3
    • 70349446579 scopus 로고    scopus 로고
    • On the trace of symmetric stable processes on Lipschitz domains
    • R. Banuelos, T. Kulczycki and B. Siudeja, On the trace of symmetric stable processes on Lipschitz domains, J. Funct. Anal. 257(10) (2009) 3329-3352.
    • (2009) J. Funct. Anal. , vol.257 , Issue.10 , pp. 3329-3352
    • Banuelos, R.1    Kulczycki, T.2    Siudeja, B.3
  • 4
    • 0001146196 scopus 로고
    • Covariant and contravariant symbols of operators
    • F. A. Berezin, Covariant and contravariant symbols of operators, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972) 1134-1167.
    • (1972) Izv. Akad. Nauk SSSR Ser. Mat. , vol.36 , pp. 1134-1167
    • Berezin, F.A.1
  • 5
    • 0038744466 scopus 로고    scopus 로고
    • Bound states for Schrödinger Hamiltonians: Phase space methods and applications
    • Ph. Blanchard and J. Stubbe, Bound States for Schrödinger Hamiltonians: Phase space method and applications, Rev. Math. Phys. 8(4) (1996) 503-547. (Pubitemid 126312445)
    • (1996) Reviews in Mathematical Physics , vol.8 , Issue.4 , pp. 503-547
    • Blanchard, P.1    Stubbe, J.2
  • 6
    • 84972491111 scopus 로고
    • The asymptotic distribution of the eigenvalues for a class of Markov operators
    • R. Blumenthal and R. Getoor, The asymptotic distribution of the eigenvalues for a class of Markov operators, Pacific J. Math. 9 (1959) 399-408.
    • (1959) Pacific J. Math. , vol.9 , pp. 399-408
    • Blumenthal, R.1    Getoor, R.2
  • 7
    • 23344440772 scopus 로고    scopus 로고
    • Two-sided eigenvalue estimates for subordinate processes in domains
    • DOI 10.1016/j.jfa.2005.05.004, PII S0022123605001977
    • Z.-Q. Chen and R. Song, Two-sided eigenvalue estimates for subordinate processes in domains, J. Funct. Anal. 226 (2005) 90-113. (Pubitemid 41102502)
    • (2005) Journal of Functional Analysis , vol.226 , Issue.1 , pp. 90-113
    • Chen, Z.-Q.1    Song, R.2
  • 11
    • 74349087923 scopus 로고    scopus 로고
    • Pólya's conjecture in the presence of a constant magnetic field
    • R. Frank, M. Loss and T. Weidl, Pólya's conjecture in the presence of a constant magnetic field, J. Eur. Math. Soc. 11 (2009) 1365-1383.
    • (2009) J. Eur. Math. Soc. , vol.11 , pp. 1365-1383
    • Frank, R.1    Loss, M.2    Weidl, T.3
  • 13
    • 64549133375 scopus 로고    scopus 로고
    • Eigenvalue inequalities for Klein-Gordon operators
    • E. M. Harrell, II and S. Yildirim Yolcu, Eigenvalue inequalities for Klein-Gordon operators, J. Funct. Anal. 256(12) (2009) 3977-3995.
    • (2009) J. Funct. Anal. , vol.256 , Issue.12 , pp. 3977-3995
    • Harrell II, E.M.1    Yildirim Yolcu, S.2
  • 14
    • 43049116937 scopus 로고    scopus 로고
    • Two new Weyl-type bounds for the Dirichlet Laplacian
    • L. Hermi, Two new Weyl-type bounds for the Dirichlet Laplacian, Trans. Amer. Math. Soc. 360 (2008) 1539-1558.
    • (2008) Trans. Amer. Math. Soc. , vol.360 , pp. 1539-1558
    • Hermi, L.1
  • 17
    • 0002697827 scopus 로고
    • Can one here the shape of a drum?
    • M. Kac, Can one here the shape of a drum? Amer. Math. Monthly 73 (1966) 1-23.
    • (1966) Amer. Math. Monthly , vol.73 , pp. 1-23
    • Kac, M.1
  • 18
    • 0031574602 scopus 로고    scopus 로고
    • Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
    • DOI 10.1006/jfan.1997.3155, PII S0022123697931554
    • A. Laptev, Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces, J. Funct. Anal. 151(2) (1997) 531-545. (Pubitemid 127172658)
    • (1997) Journal of Functional Analysis , vol.151 , Issue.2 , pp. 531-545
    • Laptev, A.1
  • 19
    • 0000538029 scopus 로고
    • On the Schrödinger equation and the eigenvalue problem
    • P. Li and S.-T. Yau, 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
  • 20
    • 84963097105 scopus 로고
    • On the eigenvalues of the vibrating membranes
    • G. Pólya, On the eigenvalues of the vibrating membranes, Proc. London Math. Soc. 11(3) (1961) 419-433.
    • (1961) Proc. London Math. Soc. , vol.11 , Issue.3 , pp. 419-433
    • Pólya, G.1
  • 23
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetzt der Eigenwerte linearer partieller Differentialgleichungen
    • H. Weyl, Das asymptotische Verteilungsgesetzt der Eigenwerte linearer partieller Differentialgleichungen, Math. Ann. 71(4) (1912) 441-479.
    • (1912) Math. Ann. , vol.71 , Issue.4 , pp. 441-479
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.