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Amrein, W. O.; Berthier, A. M.; Georgescu, V.

\(L^ p-\)inequalities for the Laplacian and unique continuation. (English) Zbl 0468.35017

Ann. Inst. Fourier 31, No. 3, 153-168 (1981).
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Cited in 29 Documents

MSC:

35B60 Continuation and prolongation of solutions to PDEs
35R45 Partial differential inequalities and systems of partial differential inequalities
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Keywords:

unique continuation properties; differential inequality; non-existence of positive eigenvalues; self-adjoint Schrödinger operators
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\textit{W. O. Amrein} et al., Ann. Inst. Fourier 31, No. 3, 153--168 (1981; Zbl 0468.35017)
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References:

[1] R.A. ADAMS, Sobolev spaces, Academic Press, New York, 1975. · Zbl 0314.46030
[2] A.M. BERTHIER, Sur le spectre ponctuel de l’opérateur de Schrödinger, C.R. Acad. Sci., Paris 290 A, (1980), 393-395 ; On the Point Spectrum of Schrödinger Operators, Ann. Sci. Ecole Normale Supérieure (to appear). · Zbl 0454.35070
[3] N. DUNFORD and J.T. SCHWARTZ, Linear operators, Part I, Interscience, New York, 1957.
[4] V. GEORGESCU, On the unique continuation property for Schrödinger Hamiltonians, Helv. Phys. Acta, 52 (1979), 655-670.
[5] G.H. HARDY, J.E. LITTELEWOOD and G. POLYA, Inequalities, Cambridge University Press, 1952. · Zbl 0047.05302
[6] E. HEINZ, Über die eindeutigkeit beim Cauchy’schen anfangswert-problem einer elliptischen differentialgleichung zweiter ordnung, Nachr. Akad.-Wiss. Göttingen, II (1955), 1-12. · Zbl 0067.07503
[7] L. HÖRMANDER, Linear partial differential operators, Springer, Berlin, 1963. · Zbl 0108.09301
[8] M. SCHECHTER and B. SIMON, Unique continuation for Schrödinger operators with unbounded potentials, J. Math. Anal. Appl., 77 (1980), 482-492. · Zbl 0458.35024
[9] E.M. STEIN and G. WEISS, Introduction to Fourier analysis on Euclidean spaces, Princeton Univ. Press, 1971. · Zbl 0232.42007
[10] H. TRIEBEL, Interpolation theory, Function Spaces, Differential Operators, North-Holland, Amsterdam, 1978. · Zbl 0387.46032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.