Geodesic
Characterization of Eigenfunctions by Boundedness Conditions
Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 204-213

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Suppose is a sequence of functions on Rn with Δfk = fk+1 (where Δ is the Laplacian) that satisfies the growth condition: |fk(x)| ≤ Mk{1 + |x|)a where a ≥ 0 and the constants have sublinear growth Then Δf0 = —f0- This characterizes eigenfunctions f of Δ with polynomial growth in terms of the size of the powers Δkf, —∞ < k < ∞. It also generalizes results of Roe (where a = 0, Mk = M, and n = 1 ) and Strichartz (where a = 0, Mk = M for n). The analogue holds for formally self-adjoint constant coefficient linear partial differential operators on Rn.
DOI : 10.4153/CMB-1992-029-x
Mots-clés : 42B10, 35B35, Eigenfunctions, Laplacian, constant coeffcient differential operators 
Howard, Ralph; Reese, Margaret. Characterization of Eigenfunctions by Boundedness Conditions. Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 204-213. doi: 10.4153/CMB-1992-029-x
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     title = {Characterization of {Eigenfunctions} by {Boundedness} {Conditions}},
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     year = {1992},
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