Abstract
Eigenfunction expansions are compared (with respect to pointwise and function space convergence) for pairs of uniformly elliptic operators with the same leading term. For two such operators, eigenfunction expansions behave in essentially the same way under analytic summation techniques. This shows, for example, that in this sense expansions in eigenfunctions of a class of elliptic operators (including Schrödinger operators) behave like the Fourier transform on R n.
Research partially supported under N.S.F. grant DMS-8509458
Research supported by Army Research Office grant number DAAG-29-84-G0004
Research supported in part by the Energy Research and Development Administration under contracts AT(11-1)-3069 and AT(40-1)-3992
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© 1987 Springer-Verlag
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Kon, M.A., Raphael, L.A., Young, J.E. (1987). On relating generalized expansions to fourier integrals. In: Knowles, I.W., Saitō, Y. (eds) Differential Equations and Mathematical Physics. Lecture Notes in Mathematics, vol 1285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080604
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DOI: https://doi.org/10.1007/BFb0080604
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