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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 $[Y_0,X_1]_{\theta,p}$ coincides with a closed subspace of $[X_0,X_1]_{\theta,p}$ when $Y_0$ is a closed subspace of codimension one. This result is applied to the study of nonharmonic Fourier series in the Sobolev spaces $H^s(-\pi,\pi)$ with $0<s<1$. The main result looks like this: if $\{e^{i\lambda_nt}\}$ is an unconditional basis in $L^2(-\pi,\pi)$, then there exist two numbers $s_0$, $s_1$ such that for $s<s_0\{e^{i\lambda_nt}\}$ forms an unconditional basis
in $H^s(-\pi,\pi)$, and for $s_1<s\{e^{i\lambda_nt}\}$ forms an unconditional basis of a closed subspace in $H^s(-\pi,\pi)$ of codimension one. If $s_0\le s\le s_1$, then the family $\{e^{i\lambda_nt}\}$ is not an unconditional basis in its span in $H^s(-\pi,\pi)$.
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
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