Characterization of Eigenfunctions by Boundedness Conditions
1992 ◽
Vol 35
(2)
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pp. 204-213
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Keyword(s):
AbstractSuppose 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.
1970 ◽
Vol 8
(2)
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pp. 195-201
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1973 ◽
Vol 49
(7)
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pp. 506-509
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1994 ◽
Vol 168
(1)
◽
pp. 19-54
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1983 ◽
Vol 8
(6)
◽
pp. 643-665
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1980 ◽
Vol 38
(1)
◽
pp. 118-138
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