메뉴 건너뛰기




Volumn 55, Issue 1, 2014, Pages

A short proof of Weyl's law for fractional differential operators

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84902258624     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.4861935     Document Type: Article
Times cited : (26)

References (25)
  • 1
    • 0001215659 scopus 로고
    • Convex functions of operators
    • F. A. Berezin, "Convex functions of operators," Mat. Sb. (N.S.) 88(130), 268-276 (1972).
    • (1972) Mat. Sb. (N.S.) , vol.88 , Issue.130 , pp. 268-276
    • Berezin, F.A.1
  • 2
    • 0003260554 scopus 로고
    • Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory
    • Series 2, American Mathematical Society, Providence, RI
    • M. Š. Birman and M. Z. Solomjak, Quantitative Analysis in Sobolev Imbedding Theorems and Applications to Spectral Theory, American Mathematical Society Translations, Series 2 Vol. 114 (American Mathematical Society, Providence, RI, 1980).
    • (1980) American Mathematical Society Translations , vol.114
    • Birman, M.Š.1    Solomjak, M.Z.2
  • 3
    • 84972491111 scopus 로고
    • The asymptotic distribution of the eigenvalues for a class of Markov operators
    • R. M. Blumenthal and R. K. Getoor, "The asymptotic distribution of the eigenvalues for a class of Markov operators," Pacific J. Math. 9, 399-408 (1959).
    • (1959) Pacific J. Math. , vol.9 , pp. 399-408
    • Blumenthal, R.M.1    Getoor, R.K.2
  • 4
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker's guide to the fractional Sobolev spaces
    • E. Di Nezza, G. Palatucci, and E. Valdinoci, "Hitchhiker's guide to the fractional Sobolev spaces," Bull. Sci. Math. 136(5), 521-573 (2012).
    • (2012) Bull. Sci. Math. , vol.136 , Issue.5 , pp. 521-573
    • Di Nezza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 5
    • 84902290752 scopus 로고    scopus 로고
    • Refined semiclassical asymptotics for fractional powers of the Laplace operator
    • (to be published); preprint arXiv:1105:5181
    • R. L. Frank and L. Geisinger, "Refined semiclassical asymptotics for fractional powers of the Laplace operator," J. Reine Angew. Math. (to be published); preprint arXiv:1105:5181.
    • J. Reine Angew. Math.
    • Frank, R.L.1    Geisinger, L.2
  • 6
    • 79960343156 scopus 로고    scopus 로고
    • Two-Term Spectral Asymptotics for the Dirichlet Laplacian on a Bounded Domain
    • (World Scientific Publishing, Hackensack, NJ
    • R. L. Frank and L. Geisinger, Two-Term Spectral Asymptotics for the Dirichlet Laplacian on a Bounded Domain, Mathematical Results in Quantum Physics (World Scientific Publishing, Hackensack, NJ, 2011), pp. 138-147.
    • (2011) Mathematical Results in Quantum Physics , pp. 138-147
    • Frank, R.L.1    Geisinger, L.2
  • 8
    • 84994112823 scopus 로고    scopus 로고
    • Geometrical versions of improved Berezin-Li-Yau inequalities
    • L. Geisinger, A. Laptev, and T. Weidl, "Geometrical versions of improved Berezin-Li-Yau inequalities," J. Spectr. Theory 1(1), 87-109 (2011).
    • (2011) J. Spectr. Theory , vol.1 , Issue.1 , pp. 87-109
    • Geisinger, L.1    Laptev, A.2    Weidl, T.3
  • 9
    • 84886817376 scopus 로고    scopus 로고
    • s on domains in d-dimensional Euclidean space
    • s on domains in d-dimensional Euclidean space," J. Math Phys. 54, 103501 (2013).
    • (2013) J. Math Phys. , vol.54 , pp. 103501
    • Hatzinikitas, A.N.1
  • 11
    • 0003306322 scopus 로고    scopus 로고
    • Microlocal Analysis and Precise Spectral Asymptotics
    • Springer-Verlag, Berlin
    • V. Ja. Ivrii, Microlocal Analysis and Precise Spectral Asymptotics, SpringerMonographs in Mathematics (Springer-Verlag, Berlin, 1998).
    • (1998) SpringerMonographs in Mathematics
    • Ivrii, V.J.1
  • 12
    • 23944449255 scopus 로고    scopus 로고
    • "Tauberian theory "Grundlehren der Mathematischen Wissenschaften
    • Springer-Verlag, Berlin
    • J. Korevaar, "Tauberian theory," Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences Vol. 329 (Springer-Verlag, Berlin, 2004).
    • (2004) Fundamental Principles of Mathematical Sciences , vol.329
    • Korevaar, J.1
  • 13
    • 62549114451 scopus 로고    scopus 로고
    • Two dimensional Berezin-Li-Yau inequalities with a correction term
    • H. Kovǎrík, S. Vugalter, and T. Weidl, "Two dimensional Berezin-Li-Yau inequalities with a correction term," Commun. Math. Phys. 287(3), 959-981 (2009).
    • (2009) Commun. Math. Phys. , vol.287 , Issue.3 , pp. 959-981
    • Kovǎrík, H.1    Vugalter, S.2    Weidl, T.3
  • 14
    • 0031574602 scopus 로고    scopus 로고
    • Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
    • A. Laptev, "Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces," J. Funct. Anal. 151(2), 531-545 (1997).
    • (1997) J. Funct. Anal. , vol.151 , Issue.2 , pp. 531-545
    • Laptev, A.1
  • 15
    • 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," Commun. Math. Phys. 88(3), 309-318 (1983).
    • (1983) Commun. Math. Phys. , vol.88 , Issue.3 , pp. 309-318
    • Li, P.1    Yau, S.T.2
  • 16
    • 0000566451 scopus 로고
    • The classical limit of quantum spin systems
    • E. H. Lieb, "The classical limit of quantum spin systems," Commun. Math. Phys. 31, 327-340 (1973).
    • (1973) Commun. Math. Phys. , vol.31 , pp. 327-340
    • Lieb, E.H.1
  • 17
    • 0242648945 scopus 로고    scopus 로고
    • Analysis
    • 2nd ed, American Mathematical Society, Providence, RI
    • E. H. Lieb and M. Loss, Analysis, 2nd ed., Graduate Studies in Mathematics Vol. 14 (American Mathematical Society, Providence, RI, 2001).
    • (2001) Graduate Studies in Mathematics , vol.14
    • Lieb, E.H.1    Loss, M.2
  • 18
    • 0037319507 scopus 로고    scopus 로고
    • A lower bound for sums of eigenvalues of the Laplacian
    • (electronic)
    • A. D. Melas, "A lower bound for sums of eigenvalues of the Laplacian," Proc. Am. Math. Soc. 131(2), 631-636 (2003) (electronic).
    • (2003) Proc. Am. Math. Soc. , vol.131 , Issue.2 , pp. 631-636
    • Melas, A.D.1
  • 20
    • 0003288250 scopus 로고    scopus 로고
    • The Asymptotic Distribution of Eigenvalues of Partial Differential Operators
    • American Mathematical Society, Providence, RI
    • Y. Safarov and D. Vassiliev, The Asymptotic Distribution of Eigenvalues of Partial Differential Operators, Translations of Mathematical Monographs Vol. 155 (American Mathematical Society, Providence, RI, 1997).
    • (1997) Translations of Mathematical Monographs , vol.155
    • Safarov, Y.1    Vassiliev, D.2
  • 21
    • 77957304530 scopus 로고    scopus 로고
    • Improved Berezin-Li-Yau inequalities with a remainder term
    • T. Weidl, "Improved Berezin-Li-Yau inequalities with a remainder term," Am. Math. Soc. Transl. 225(2), 253-263 (2008).
    • (2008) Am. Math. Soc. Transl. , vol.225 , Issue.2 , pp. 253-263
    • Weidl, T.1
  • 22
    • 0001117305 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)
    • H. Weyl, "Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung)," Math. Ann. 71(4), 441-479 (1912).
    • (1912) Math. Ann. , vol.71 , Issue.4 , pp. 441-479
    • Weyl, H.1
  • 23
    • 84859130342 scopus 로고    scopus 로고
    • Bounds for the eigenvalues of the fractional Laplacian
    • S. Yildirim Yolcu and T. Yolcu, "Bounds for the eigenvalues of the fractional Laplacian," Rev. Math. Phys. 24(3), 1250003 (2012).
    • (2012) Rev. Math. Phys. , vol.24 , Issue.3 , pp. 1250003
    • Yildirim Yolcu, S.1    Yolcu, T.2
  • 24
    • 84874385940 scopus 로고    scopus 로고
    • Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain
    • S. Yildirim Yolcu and T. Yolcu, "Estimates for the sums of eigenvalues of the fractional Laplacian on a bounded domain," Commun. Contemp. Math. 15(3), 1250048 (2013).
    • (2013) Commun. Contemp. Math. , vol.15 , Issue.3 , pp. 1250048
    • Yildirim Yolcu, S.1    Yolcu, T.2
  • 25
    • 84884796478 scopus 로고    scopus 로고
    • Refined bounds for the eigenvalues of the Klein-Gordon operator
    • T. Yolcu, "Refined bounds for the eigenvalues of the Klein-Gordon operator," Proc. Am. Math. Soc. 141(12), 4305-4315 (2013).
    • (2013) Proc. Am. Math. Soc. , vol.141 , Issue.12 , pp. 4305-4315
    • Yolcu, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.