메뉴 건너뛰기




Volumn 2016, Issue 712, 2016, Pages 1-37

Refined semiclassical asymptotics for fractional powers of the Laplace operator

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84961842272     PISSN: 00754102     EISSN: 14355345     Source Type: Journal    
DOI: 10.1515/crelle-2013-0120     Document Type: Article
Times cited : (47)

References (22)
  • 2
    • 70349446579 scopus 로고    scopus 로고
    • On the trace of symmetric stable processes on Lipschitz domains
    • R. Bañuelos, T. Kulczycki and B. Siudeja, On the trace of symmetric stable processes on Lipschitz domains, J. Funct. Anal. 257 (2009), no. 10, 3329-3352.
    • (2009) J. Funct. Anal. , vol.257 , Issue.10 , pp. 3329-3352
    • Bañuelos, R.1    Kulczycki, T.2    Siudeja, B.3
  • 3
    • 0001146196 scopus 로고
    • Covariant and contravariant symbols of operators
    • F. A. Berezin, Covariant and contravariant symbols of operators, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1972), 1134-1167.
    • (1972) Izv. Akad. Nauk SSSR Ser. Mat. , vol.13 , pp. 1134-1167
    • Berezin, F.A.1
  • 4
    • 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 (1959), 399-408.
    • (1959) Pacific J. Math. , vol.9 , pp. 399-408
    • Blumenthal, R.M.1    Getoor, K.R.2
  • 5
    • 23344440772 scopus 로고    scopus 로고
    • Two-sided eigenvalue estimates for subordinate processes in domains
    • Z. Chen and R. Song, Two-sided eigenvalue estimates for subordinate processes in domains, J. Funct. Anal. 226 (2005), no. 1, 90-113.
    • (2005) J. Funct. Anal. , vol.226 , Issue.1 , pp. 90-113
    • Chen, Z.1    Song, R.2
  • 8
    • 0000667789 scopus 로고
    • An operator inequality
    • F. Hansen, An operator inequality, Math. Ann. 246 (1980), no. 3, 249-250.
    • (1980) Math. Ann , vol.246 , Issue.3 , pp. 249-250
    • Hansen, F.1
  • 9
    • 0141987268 scopus 로고
    • The analysis of linear partial differential operators
    • Springer-Verlag Berlin
    • L. Hörmander, The analysis of linear partial differential operators. IV: Fourier integral operators, Springer- Verlag, Berlin 1985.
    • (1985) IV: Fourier Integral Operators
    • Hörmander, L.1
  • 10
    • 84931319071 scopus 로고
    • The second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary and for elliptic operators acting in vector bundles
    • V. J. Ivrii, The second term of the spectral asymptotics for the Laplace-Beltrami operator on manifolds with boundary and for elliptic operators acting in vector bundles, Soviet Math. Dokl. 20 (1980), no. 1, 1300-1302.
    • (1980) Soviet Math. Dokl. , vol.20 , Issue.1 , pp. 1300-1302
    • Ivrii, V.J.1
  • 12
    • 82755165257 scopus 로고    scopus 로고
    • Spectral analysis of subordinate Brownian motions on the half-line
    • M. Kwásnicki, Spectral analysis of subordinate Brownian motions on the half-line, Studia Math. 206 (2011), no. 3, 211-271.
    • (2011) Studia Math. , vol.206 , Issue.3 , pp. 211-271
    • Kwásnicki, M.1
  • 13
    • 84855892829 scopus 로고    scopus 로고
    • Eigenvalues of the fractional laplace operator in the interval
    • M. Kwásnicki, Eigenvalues of the fractional laplace operator in the interval, J. Funct. Anal. 262 (2012), no. 5, 2379-2402.
    • (2012) J. Funct. Anal. , vol.262 , Issue.5 , pp. 2379-2402
    • Kwásnicki, M.1
  • 14
    • 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), no. 3, 309-318.
    • (1983) Comm. Math. Phys. , vol.88 , Issue.3 , pp. 309-318
    • Li, P.1    Yau, S.T.2
  • 15
    • 0000566451 scopus 로고
    • The classical limit of quantum spin systems
    • E. H. Lieb, The classical limit of quantum spin systems, Comm. Math. Phys. 31 (1973), 327-340.
    • (1973) Comm. Math. Phys. , vol.31 , pp. 327-340
    • Lieb, E.H.1
  • 16
    • 0002667676 scopus 로고
    • The stability and instability of relativistic matter
    • E. H. Lieb and H. T. Yau, The stability and instability of relativistic matter, Comm. Math. Phys. 118 (1988), no. 2, 177-213.
    • (1988) Comm. Math. Phys. , vol.118 , Issue.2 , pp. 177-213
    • Lieb, E.H.1    Yau, H.T.2
  • 17
    • 0003256486 scopus 로고
    • Inequalities: Theory of majorization and its applications
    • Academic Press, New York
    • A.W. Marshall and I. Olkin, Inequalities: Theory of majorization and its applications, Math. Sci. Eng. 143, Academic Press, New York 1979.
    • (1979) Math. Sci. Eng. , vol.143
    • Marshall, A.W.1    Olkin, I.2
  • 18
    • 44649191975 scopus 로고    scopus 로고
    • The scattering matrix and the differences of spectral projections
    • A. Pushnitski, The scattering matrix and the differences of spectral projections, Bull. Lond. Math. Soc. 40 (2008), 227-238.
    • (2008) Bull. Lond. Math. Soc. , vol.40 , pp. 227-238
    • Pushnitski, A.1
  • 20
    • 0003327082 scopus 로고    scopus 로고
    • The asymptotic distribution of eigenvalues of partial differential operators
    • American Mathematical Society, Providence
    • Y. Safarov and D. Vassiliev, The asymptotic distribution of eigenvalues of partial differential operators, Transl. Math. Monogr. 155, American Mathematical Society, Providence 1996.
    • (1996) Transl. Math. Monogr. , vol.155
    • Safarov, Y.1    Vassiliev, D.2
  • 22
    • 0242593273 scopus 로고    scopus 로고
    • A new coherent states approach to semiclassics which gives Scotts correction
    • J. P. Solovej and W. L. Spitzer, A new coherent states approach to semiclassics which gives Scotts correction, Comm. Math. Phys 241 (2003), 383-420.
    • (2003) Comm. Math. Phys , vol.241 , pp. 383-420
    • Solovej, J.P.1    Spitzer, W.L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.