Interpolation of subspaces and applications to exponential bases in Sobolev spaces

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dc.creatorIvanov, S.
dc.creatorKalton, N.
dc.date2001-04-12
dc.date.accessioned2026-07-07T04:41:16Z
dc.date.available2026-07-07T04:41:16Z
dc.descriptionWe give precise conditions under which the real interpolation space [Y_0,X_1]_{s,p} coincides with a closed subspace of the corresponding interpolation space [X_0,X_1]_{s,p} when Y_0 is a closed subspace of X_0 of codimension one. This result is applied to study the basis properties of nonharmonic Fourier series in Sobolev spaces H^s on an interval when 0<s<1. The main result: let E be a family of exponentials exp(i λ_n t) and E forms an unconditional basis in L^2 on an interval. Then there exist two number s_0, s_1 such that E forms an unconditional basis in H^s for s<s_0, E forms an unconditional basis in its span with codimension 1 in H^s for s_1<s. For s in [s_0,s_1] the exponential family is not an unconditional basis in its span.
dc.description23 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/math/0104130
dc.identifierhttp://arxiv.org/abs/math/0104130
dc.identifierS.Petersburg Math. J. (Algebra i Analiz) v.13, no.2, pp. 93-115
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61289
dc.subjectFunctional Analysis
dc.subject46B70 (Primary) 42C15 (Secondary)
dc.titleInterpolation of subspaces and applications to exponential bases in Sobolev spaces
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