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On some properties of solutions of Helmholtz equation
dc.contributor.authorRamm, A. G.en_US
dc.date.accessioned2010-05-06T20:53:39Z
dc.date.available2010-05-06T20:53:39Z
dc.date.issued1981-02en_US
dc.identifier.citationRamm, A. G. (1981). "On some properties of solutions of Helmholtz equation." Journal of Mathematical Physics 22(2): 275-276. <http://hdl.handle.net/2027.42/69628>en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/69628
dc.description.abstractWe give a new method to prove results of the following type. Let: (∇2 + k2)u=0 in DR={x‖x‖?R}, k2≳0. (1) If u∊L2(DR), then u≡0 in DR. (2) If ‖x‖mu(x)→0 as ‖x‖→∞, x21+⋅⋅⋅+x2N−1?cx−2pN ,p≳0, m=1, 2, 3,..., ‖x‖[(∂u/∂‖x‖)−iku‖x‖→∞]→0, then u≡0 in DR.en_US
dc.format.extent3102 bytes
dc.format.extent103123 bytes
dc.format.mimetypetext/plain
dc.format.mimetypeapplication/pdf
dc.publisherThe American Institute of Physicsen_US
dc.rights© The American Institute of Physicsen_US
dc.titleOn some properties of solutions of Helmholtz equationen_US
dc.typeArticleen_US
dc.subject.hlbsecondlevelPhysicsen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumUniversity of Michigan, Department of Mathematics, Ann Arbor, Michigan 48109en_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/69628/2/JMAPAQ-22-2-275-1.pdf
dc.identifier.doi10.1063/1.524900en_US
dc.identifier.sourceJournal of Mathematical Physicsen_US
dc.identifier.citedreferenceO. Arena and W. Littman, “Farfield behavior of solution to P. D. E.,” Ann. Sc. Norm. Super. Pisa 2B, 807–27 (1972).en_US
dc.identifier.citedreferenceT. Kato, “Growth properties of solutions of the reduced wave equation with variable coefficient,” Commun. Pure Appl. Math. 12, 402–25 (1959).en_US
dc.identifier.citedreferenceA. G. Ramm, “About the absence of the discrete positive spectrum of the Laplace operator of the Dirichlet problem in some domains with infinite boundaries,” Vestn. Leningr. Univ. Mat. Mekh. Astron. 13, 153–6 (1964); 1, 176 (1966).en_US
dc.identifier.citedreferenceA. G. Ramm, “Nonselfadjoint operators in diffraction and scattering,” Math. Meth. Appl. Sci. 2, 327–46 (1980).en_US
dc.identifier.citedreferenceA. G. Ramm, Theory and Applications of Some New Classes of Integral Equations (Springer, New York, 1980).en_US
dc.owningcollnamePhysics, Department of


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