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Eigenfunction expansions associated with the Laplacian for certain domains with infinite boundaries. I


Author: Charles Irwin Goldstein
Journal: Trans. Amer. Math. Soc. 135 (1969), 1-31
MSC: Primary 35.80
MathSciNet review: 0234140
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  • [1] Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers John Wiley & Sons, Inc. New York-London-Sydney, 1964. MR 0163043
  • [2] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. MR 0065391
  • [3] D. M. Eidus, The principle of limiting absorption, Amer. Math. Soc. Transl. 47 (1965), 157-192.
  • [4] Kurt Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), no. 1, 465–487 (German). MR 1512905, 10.1007/BF01449150
  • [5] Teruo Ikebe, Orthogonality of the eigenfunctions for the exterior problem connected with 𝑚𝑖𝑛𝑢𝑠\triangle, Arch. Rational Mech. Anal. 19 (1965), 71–73. MR 0178236
  • [6] Teruo Ikebe, Eigenfunction expansions associated with the Schroedinger operators and their applications to scattering theory, Arch. Rational Mech. Anal. 5 (1960), 1–34 (1960). MR 0128355
  • [7] D. S. Jones, The eigenvalues of ∇²𝑢+𝜆𝑢=0 when the boundary conditions are given on semi-infinite domains, Proc. Cambridge Philos. Soc. 49 (1953), 668–684. MR 0058086
  • [8] P. D. Lax, A Phragmén-Lindelöf theorem in harmonic analysis and its application to some questions in the theory of elliptic equations, Comm. Pure Appl. Math. 10 (1957), 361–389. MR 0093706
  • [9] Peter D. Lax and Ralph S. Phillips, Scattering theory, Bull. Amer. Math. Soc. 70 (1964), 130–142. MR 0167868, 10.1090/S0002-9904-1964-11051-X
  • [10] Carlo Miranda, Equazioni alle derivate parziali di tipo ellittico, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 2, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1955 (Italian). MR 0087853
  • [11] Franz Rellich, Über das asymptotische Verhalten der Lösungen von Δ𝑢+𝜆𝑢=0 in unendlichen Gebieten, Jber. Deutsch. Math. Verein. 53 (1943), 57–65 (German). MR 0017816
  • [12] A. A. Samarskiy and A. N. Tikhonov, On excitation of radio wave guides, Akad. Nauk SSSR. Ž. Tehn. Fiz. 17 (1947), 1283-1296.
  • [13] Norman A. Shenk II, Eigenfunction expansions and scattering theory for the wave equation in an exterior region, Arch. Rational Mech. Anal. 21 (1966), 120–150. MR 0187631
  • [14] Yasushi Shizuta, Eigenfunction expansion associated with the operator -𝛿 in the exterior domain, Proc. Japan Acad. 39 (1963), 656–660. MR 0195420
  • [15] S. L. Sobolev, Some applications of functional analysis in mathematical physics, Transl. Math. Monographs, Vol. 7, Amer. Math. Soc., Providence, R. I., 1963.
  • [16] Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877
  • [17] E. Titchmarsh, Introduction to the theory of Fourier integrals, Oxford Univ. Press, London, 1937.

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DOI: https://doi.org/10.1090/S0002-9947-1969-0234140-4
Article copyright: © Copyright 1969 American Mathematical Society