@article{ASENS_1982_4_15_3_441_0,
author = {Urakawa, Hajime},
title = {Bounded domains which are isospectral but not congruent},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {441--456},
year = {1982},
publisher = {Elsevier},
volume = {Ser. 4, 15},
number = {3},
doi = {10.24033/asens.1433},
mrnumber = {84g:58106},
zbl = {0505.58036},
language = {en},
url = {https://www.numdam.org/articles/10.24033/asens.1433/}
}
TY - JOUR AU - Urakawa, Hajime TI - Bounded domains which are isospectral but not congruent JO - Annales scientifiques de l'École Normale Supérieure PY - 1982 SP - 441 EP - 456 VL - 15 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.24033/asens.1433/ DO - 10.24033/asens.1433 LA - en ID - ASENS_1982_4_15_3_441_0 ER -
%0 Journal Article %A Urakawa, Hajime %T Bounded domains which are isospectral but not congruent %J Annales scientifiques de l'École Normale Supérieure %D 1982 %P 441-456 %V 15 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.24033/asens.1433/ %R 10.24033/asens.1433 %G en %F ASENS_1982_4_15_3_441_0
Urakawa, Hajime. Bounded domains which are isospectral but not congruent. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 15 (1982) no. 3, pp. 441-456. doi: 10.24033/asens.1433
[A] , Lecture Notes on Elliptic Boundary Value Problems (van Nostrand Company, Toronto-Princeton-New York-London, 1965). | Zbl | MR
[B1] , Spectres et groupes cristallographiques I: domaines euclidiens (Invent. Math., Vol. 58, 1980, pp. 179-199). | Zbl | MR
[B2] , Remarque sur la conjecture de Weyl (to appear in Compositio Math.). | Numdam
[B.B.] and , Spectres et groupes cristallographiques II: domaines sphériques (Ann. Inst. Fourier, Grenoble, Vol. 30, No. 3, 1980, pp. 237-248). | Zbl | MR | Numdam
[Br] , Eigenvalues of the Laplacian (Amer. Math. Soc., Proc. Pure Math., Vol. 16, 1970, pp. 121-125). | Zbl | MR
[B.G.M.] , and , Le spectre d'une variété riemannienne (Lecture Notes in Math., No. 194, Springer-Verlag, Berlin-Heiderberg-New York, 1970). | Zbl | MR
[B.N.] , Groupes et algèbres de Lie, Chapitres 4 à 6, Hermann, Paris, 1968.
, Extended Asymptotic Eigenvalue Distributions for Bounded Domains in n-Space (J. Math. Mech., Vol. 6, 1957, pp. 119-166). | Zbl | MR
[C] , Über die asymptotische Verteilung der Eigenwerte partieller Differential gleichungen (Ber. der Sachs. Acad. d. Wiss. Leipzig, Vol. 88, 1936, pp. 119-132). | Zbl | JFM
[E] , A Construction of Non-Flat Compact Irreducible Riemannian Manifolds which are Isospectral But not Isometric (Math. Z., Vol. 168, 1979, pp. 207-212). | Zbl | MR | EuDML
[F] , Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicher Spannung die kreisförmige den tiefsten Grundton gibt (Sitz. ber. bayer. Acad. Wiss., 1923, pp. 169-172). | JFM
[Gd] , Boundary Value Problems in Non-Smooth Domains (Lecture Notes, No. 19, Univ. Maryland, Depart. Math., College Park, 1980).
[G] , Über die asymptotische Verteilung der Eigenwerte des Laplace-Operators fur Gebiete auf der Kugeloberfläche (Math. Z., Vol. 94, 1966, pp. 110-121). | Zbl | MR | EuDML
[I] , On Lens Spaces which are Isospectral But not Isometric (Ann. scient. Éc. Norm. Sup., 4e série, t. 13, 1980, pp. 303-315). | Numdam | Zbl | MR | EuDML
[K] , Can One Hear the Shape of a Drum? (Amer. Math. Monthly, Vol. 73, 1966, pp. 1-23). | Zbl | MR
[Kr] , Ueber Minimaleigenschaften der Kugel in drei und mehr Dimensionen (Acta Comm. Univ. Tartu (Dorpat), Vol. 9, 1926, p. 1-144). | JFM
[M.S.] and , Curvature and the Eigenvalues of the Laplacian (J. Diff. Geometry, Vol. 1, 1967, pp. 43-69). | Zbl | MR
[M] , Eigenvalues of the Laplace Operator on Certain Manifolds (Proc. Nat. Acad. Sc., Vol. 51, 1964, p. 542). | Zbl | MR
[P] , Neue Herleitung der Sturm-Liouvilleschen Reihenentwicklung stetiger Functionen (Math. Ann., Vol. 95, 1926, pp. 499-518). | JFM | EuDML
[V] , Variétés riemanniennes isospectrales et non isométriques (Ann. Math., Vol. 112, 1980, pp. 21-32). | Zbl | MR
[Wr] , An Isoperimetric Inequality for the N-dimensional Free Membrane Problem (J. Rat. Mech. Anal., Vol. 5, 1956, pp. 533-536). | Zbl | MR
[W] , Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalten elastische Körpers (Rendiconti. Circ. Math. Palermo, Vol. 39, 1915, pp. 1-50). | JFM
[Yau] , Problem section, Institute for Advanced Study, Princeton (to appear in Annals of Math. Studies).
[Y] , Methods of Solving Differential Equations (in Japanese), 2nd ed. (Iwanami, Tokyo, 1978).
Cité par Sources :






