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Eigenfunctions of Laplace operators. (English) Zbl 0275.58003


MSC:

58B15 Fredholm structures on infinite-dimensional manifolds
58J99 Partial differential equations on manifolds; differential operators
47F05 General theory of partial differential operators
Full Text: DOI

References:

[1] Ralph Abraham, Transversality in manifolds of mappings, Bull. Amer. Math. Soc. 69 (1963), 470 – 474. · Zbl 0171.44501
[2] Shmuel Agmon, Lectures on elliptic boundary value problems, Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. · Zbl 0142.37401
[3] J. H. Albert, Nodal and critical sets for eigenfunctions of elliptic operators, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 71 – 78.
[4] N. Aronszajn, A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order, J. Math. Pures Appl. (9) 36 (1957), 235 – 249. · Zbl 0084.30402
[5] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. I, Interscience Publishers, Inc., New York, N.Y., 1953. · Zbl 0051.28802
[6] Frank Quinn, Transversal approximation on Banach manifolds, Global Analysis (Proc. Sympos. Pure Math., Vol. XV, Berkeley, Calif., 1968), Amer. Math. Soc., Providence, R.I., 1970, pp. 213 – 222.
[7] K. Uhlenbeck, Generic properties of eigenfunctions (in preparation). · Zbl 0355.58017
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