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Volumn 18, Issue 5, 2000, Pages 447-475

Plane Domains which are Spectrally Determined

Author keywords

Eigenvalues of the Laplacian; Planar drum problem; Trace of the heat kernel

Indexed keywords


EID: 0010667117     PISSN: 0232704X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006641021540     Document Type: Article
Times cited : (19)

References (17)
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    • Gordon, C.1    Webb, D.2    Wolpert, S.3
  • 5
    • 0000724778 scopus 로고
    • An asymptotic expansion for the heat equation
    • Greiner, P.: An asymptotic expansion for the heat equation, Arch. Rational Mech. Anal. 41 (1971), 163-218.
    • (1971) Arch. Rational Mech. Anal. , vol.41 , pp. 163-218
    • Greiner, P.1
  • 6
    • 0002697827 scopus 로고
    • Can one hear the shape of a drum?
    • Kac, M.: Can one hear the shape of a drum?, Amer. Math. Mon. 73 (1966), 1-23.
    • (1966) Amer. Math. Mon. , vol.73 , pp. 1-23
    • Kac, M.1
  • 7
    • 0010704376 scopus 로고
    • Mouvement Brownier et valeurs propers due Laplacian
    • Louchard, G.: Mouvement Brownier et valeurs propers due Laplacian, Inst. Henri Poincaré Annales B 4 (1968), 331-342.
    • (1968) Inst. Henri Poincaré Annales B , vol.4 , pp. 331-342
    • Louchard, G.1
  • 8
    • 84972530647 scopus 로고
    • Curvature and eigenvalues of the Laplacian
    • McKean, H. P. and Singer, I. M.: Curvature and eigenvalues of the Laplacian, J. Differential Geom. 1 (1967), 43-69.
    • (1967) J. Differential Geom. , vol.1 , pp. 43-69
    • McKean, H.P.1    Singer, I.M.2
  • 9
    • 0000328519 scopus 로고
    • Some properties of the eigenfunctions of the Laplace operator on Riemanian manifolds
    • Minakshisundarum, S. and Pleijel, A.: Some properties of the eigenfunctions of the Laplace operator on Riemanian manifolds, Canad. J. Math. 1 (1949), 242-256.
    • (1949) Canad. J. Math. , vol.1 , pp. 242-256
    • Minakshisundarum, S.1    Pleijel, A.2
  • 10
    • 0041740023 scopus 로고
    • Geometry of the Laplace operator
    • in T. Kotake (ed.)
    • Ozawa, S.: Geometry of the Laplace operator, in T. Kotake (ed.), Reports on Global Analysis 3, 1981, pp. 1-175.
    • (1981) Reports on Global Analysis , vol.3 , pp. 1-175
    • Ozawa, S.1
  • 11
    • 78651339290 scopus 로고
    • A study of certain Green's functions with applications in the theory of vibrating membranes
    • Pleijel, A.: A study of certain Green's functions with applications in the theory of vibrating membranes, Ark. Mat. 2(29) (1952), 553-569.
    • (1952) Ark. Mat. , vol.2 , Issue.29 , pp. 553-569
    • Pleijel, A.1
  • 12
    • 0001441799 scopus 로고
    • The resolvent of an elliptic boundary problem
    • Seeley, R.: The resolvent of an elliptic boundary problem, Amer. J. Math. 91 (1969), 889-919.
    • (1969) Amer. J. Math. , vol.91 , pp. 889-919
    • Seeley, R.1
  • 13
    • 0001519691 scopus 로고
    • The asymptotics of the heat equation for a boundary value problem
    • Smith, L.: The asymptotics of the heat equation for a boundary value problem, Invent. Math. 63 (1981), 467-493.
    • (1981) Invent. Math. , vol.63 , pp. 467-493
    • Smith, L.1
  • 15
    • 0001962307 scopus 로고
    • Equilibrium states of elastic rings
    • Tadjbakhsh, I. and Odeh, F.: Equilibrium states of elastic rings, J. Math. Anal. Appl. 18 (1967), 59-74.
    • (1967) J. Math. Anal. Appl. , vol.18 , pp. 59-74
    • Tadjbakhsh, I.1    Odeh, F.2
  • 17
    • 52149116800 scopus 로고
    • Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers
    • Weyl, H.: Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers, Rend. Circ. Mat. Palermo 39 (1950), 1-50.
    • (1950) Rend. Circ. Mat. Palermo , vol.39 , pp. 1-50
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.