|
This article is cited in 22 scientific papers (total in 22 papers)
Research Papers
Interpolation of subspaces and applications to exponential bases
S. Ivanova, N. Kaltonb a Russian Center of Laser Physics, St. Petersburg State University, St. Petersburg, Russia
b Department of Mathematics, University of Missouri, Columbia, USA
Abstract:
Precise conditions are given under which the real interpolation space [Y0,X1]θ,p coincides with a closed subspace of [X0,X1]θ,p when Y0 is a closed subspace of codimension one. This result is applied to the study of nonharmonic Fourier series in the Sobolev spaces Hs(−π,π) with 0<s<1. The main result looks like this: if {eiλnt} is an unconditional basis in L2(−π,π), then there exist two numbers s0, s1 such that for s<s0{eiλnt} forms an unconditional basis
in Hs(−π,π), and for s1<s{eiλnt} forms an unconditional basis of a closed subspace in Hs(−π,π) of codimension one. If s0⩽s⩽s1, then the family {eiλnt} is not an unconditional basis in its span in Hs(−π,π).
Keywords:
Riesz basis, Sobolev space, K-functional, Muckenhoupt condition, nonharmonic Fourier series.
Received: 10.09.2000
Citation:
S. Ivanov, N. Kalton, “Interpolation of subspaces and applications to exponential bases”, Algebra i Analiz, 13:2 (2001), 93–115; St. Petersburg Math. J., 13:2 (2002), 221–239
Linking options:
https://www.mathnet.ru/eng/aa927 https://www.mathnet.ru/eng/aa/v13/i2/p93
|
Statistics & downloads: |
Abstract page: | 545 | Full-text PDF : | 185 | References: | 2 | First page: | 1 |
|