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Algebra i Analiz, 2001, Volume 13, Issue 2, Pages 93–115 (Mi aa927)  

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 s0ss1, 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
Bibliographic databases:
Document Type: Article
Language: English
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
Citation in format AMSBIB
\Bibitem{IvaKal01}
\by S.~Ivanov, N.~Kalton
\paper Interpolation of subspaces and applications to exponential bases
\jour Algebra i Analiz
\yr 2001
\vol 13
\issue 2
\pages 93--115
\mathnet{http://mi.mathnet.ru/aa927}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1834861}
\zmath{https://zbmath.org/?q=an:1014.46046}
\transl
\jour St. Petersburg Math. J.
\yr 2002
\vol 13
\issue 2
\pages 221--239
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  • https://www.mathnet.ru/eng/aa927
  • https://www.mathnet.ru/eng/aa/v13/i2/p93
  • This publication is cited in the following 22 articles:
    1. S. V. Astashkin, “Spectral properties of the dilation operator in rearrangement invariant spaces of fundamental type”, Siberian Math. J., 64:1 (2023), 1–12  mathnet  crossref  crossref
    2. Astashkin S.V., “Symmetric Finite Representability of l(P)-Spaces in Rearrangement Invariant Spaces on (0, Infinity)”, Math. Ann., 383:3-4 (2022), 1489–1520  crossref  isi  scopus
    3. Astashkin V S., “A Characterization of l(P)-Spaces Symmetrically Finitely Represented in Symmetric Sequence Spaces”, Banach J. Math. Anal., 16:2 (2022), 30  crossref  mathscinet  isi
    4. Zerulla K., “Interpolation of a Regular Subspace Complementing the Span of a Radially Singular Function”, Studia Math., 2022  crossref  mathscinet  isi
    5. Asekritova I., Kruglyak N., “Necessary and Sufficient Conditions for Invertibility of Operators in Spaces of Real Interpolation”, J. Funct. Anal., 264:1 (2013), 207–245  crossref  mathscinet  zmath  isi  elib  scopus
    6. V. V. Vlasov, D. A. Medvedev, “Functional-differential equations in Sobolev spaces and related problems of spectral theory”, Journal of Mathematical Sciences, 164:5 (2010), 659–841  mathnet  crossref  mathscinet  elib
    7. Astashkin S.V., Sunehag P., “Real method of interpolation on subcouples of codimension one”, Studia Math., 185:2 (2008), 151–168  crossref  mathscinet  zmath  isi  elib  scopus
    8. Asekritova I., Kruglyak N., “Invertibility of operators in spaces of real interpolation”, Rev. Mat. Complut., 21:1 (2008), 207–217  crossref  mathscinet  zmath  isi  elib  scopus
    9. Parfenov A.I., “O suschestvovanii szhimayuschego otobrazheniya, sokhranyayuschego granichnye znacheniya”, Vestn. Novosibirskogo gos. un-ta. Ser.: Matem., mekh., inform., 7:2 (2007), 65–87  mathscinet  zmath
    10. Astashkin S.V., “Interpolyatsiya podprostranstv korazmernosti odin”, Vestn. Samarskogo gos. un-ta, 2007, no. 9-1, 75–84  mathscinet  zmath
    11. A. I. Parfenov, “O suschestvovanii szhimayuschego otobrazheniya, sokhranyayuschego granichnye znacheniya”, Vestn. NGU. Ser. matem., mekh., inform., 7:2 (2007), 65–87  mathnet
    12. S. V. Astashkin, P. Sunehag, “The Real Interpolation Method on Couples of Intersections”, Funct. Anal. Appl., 40:3 (2006), 218–221  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. S. V. Astashkin, “Interpolation of Intersections Generated by a Linear Functional”, Funct. Anal. Appl., 39:2 (2005), 131–134  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. S. V. Astashkin, “Interpolation of intersections by the real method”, St. Petersburg Math. J., 17:2 (2006), 239–265  mathnet  crossref  mathscinet  zmath
    15. Guo B.Z., Ivanov S.A., “Boundary controllability and observability of a one-dimensional nonuniform SCOLE system”, J. Optim. Theory Appl., 127:1 (2005), 89–108  crossref  mathscinet  zmath  isi  elib  scopus
    16. Sunehag P., “Subcouples of codimension one and interpolation of operators that almost agree”, J. Approx. Theory, 130:1 (2004), 78–98  crossref  mathscinet  zmath  isi  scopus
    17. A. I. Parfenov, “On an embedding criterion for interpolation spaces and application to indefinite spectral problems”, Siberian Math. J., 44:4 (2003), 638–644  mathnet  crossref  mathscinet  zmath  isi
    18. Kaijser S., Sunehag P., “Interpolation of Banach algebras and tensor products of Banach couples”, J. Math. Anal. Appl., 278:2 (2003), 367–375  crossref  mathscinet  zmath  isi  scopus
    19. V. V. Vlasov, S. A. Ivanov, “Sobolev space estimates for solutions of equations with retardation, and a basis built from divided differences”, St. Petersburg Math. J., 15:4 (2004), 545–561  mathnet  crossref  mathscinet  zmath
    20. V. V. Vlasov, S. A. Ivanov, “Estimates of Solutions to Equations with Aftereffect in Sobolev Spaces and the Basis of Divided Differences”, Math. Notes, 72:2 (2002), 271–274  mathnet  crossref  crossref  mathscinet  zmath  isi
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