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Asymptotic distribution of eigenvalues and eigenfunctions for general linear elliptic boundary value problems


Author: Bui An Ton
Journal: Trans. Amer. Math. Soc. 122 (1966), 516-546
MSC: Primary 35.80; Secondary 35.45
DOI: https://doi.org/10.1090/S0002-9947-1966-0198016-0
MathSciNet review: 0198016
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  • [1] S. Agmon, On the eigenfunctions and on the eigenvalues of general elliptic boundary value problem, Comm. Pure Appl. Math. 15 (1962), 119-147. MR 0147774 (26:5288)
  • [2] S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I, Comm. Pure Appl. Math. 12 (1959), 623-727. MR 0125307 (23:A2610)
  • [3] F. Browder, Estimates and existence theorems for elliptic boundary value problems, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 365-372. MR 0132913 (24:A2749)
  • [4] -, The spectral theory of strongly elliptic differential operators, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 1413-1422. MR 0142901 (26:468)
  • [5] -, On the spectral theory of elliptic differential operators. I, Math. Ann. 142 (1961), 22-127. MR 0209909 (35:804)
  • [6] -, A priori estimates for solutions of elliptic boundary value problems. I, II, Indag. Math. 22 (1960), 145-169. MR 0123819 (23:A1141)
  • [7] T. Carleman, Propriétés asymptotiques des fonctions fondamentales des membranes vibrantes, Attonde Skand. Matematikerekongrussen, Stockholm, 1934, pp. 34-44.
  • [8] -, Über die symptotische verteilung der Eigenwerte partieller Differentialgleichungen, Ber. Verh. Sächs. Akad. Wiss. Leipzig Math.-Nat. Kl. 88 (1936), 119-132.
  • [9] L. Gårding, On the asymptotic distribution of the eigenvalues and eigenfunctions of elliptic differential operators, Math. Scand. 1 (1953), 237-255. MR 0064980 (16:366b)
  • [10] G. H. Hardy and T. E. Littlewood, Notes on the theory of series (XI): On Tauberian theorems, Proc. London Math. Soc. (2) 30 (1930), 23-27.
  • [11] M. V. Keldych, On the eigenvalues and eigenfunctions of some classes of non-self-adjoint equations, Dokl. Akad. Nauk SSSR 77 (1951), 11-14.
  • [12] E. E. Levi, Sulle equationi lineari totalmette ellittiche alle derivate parziali, Rend. Circ Mat. Palermo. 24 (1907), 275-317.
  • [13] A. F. Ruston, The Fredholm theory of integral equations for equations belonging to the trace class of a general Banach space, Proc. London Math. Soc. 53 (1951), 109-124. MR 0042612 (13:138c)
  • [14] M. Schechter, General boundary value problems for elliptic partial differential equations, Comm. Pure Appl. Math. 12 (1959), 457-486. MR 0125323 (23:A2626)
  • [15] S. Agmon, On kernels and eigenfunctions of operators related to elliptic problems, Comm. Pure Appl. Math. 18 (1965), 559-579(2). MR 0198287 (33:6446)
  • [16] F. Browder, Asymptotic distribution of eigenvalues and eigenfunctions for non-local elliptic boundary value problems. I, Amer. J. Math. 57 (1965), 175-195(2). MR 0174858 (30:5049)

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DOI: https://doi.org/10.1090/S0002-9947-1966-0198016-0
Article copyright: © Copyright 1966 American Mathematical Society

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