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An application of the hausdorff-young inequality to eigenfunction expansions

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Part of the Lecture Notes in Mathematics book series (LNM,volume 415)

Keywords

  • Banach Space
  • Equivalence Class
  • Orthonormal System
  • Finite Rank
  • Eigenfunction Expansion

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References

  1. N. Bari, Sur les systèmes complets de fonctions orthogonales, Mat. Sbornik 14(1944), 51–108.

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  2. H. E. Benzinger, Perturbation of bases, the Hausdorff-Young inequality, and eigenfunction expansions, in preparation.

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  3. G. D. Birkhoff, A theorem on series of orthogonal functions with an application to Sturm-Liouville series, Proc. Nat. Acad. of Sci. 3 (1917), 656–659.

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  4. J. Kazdan, Perturbation of complete orthonormal sets and eigenfunction expansions, Proc. Amer. Math. Soc. 27(1971), 506–510. MR 42 # 6648.

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  5. J. L. Walsh, On the convergence of Sturm-Liouville series, Annals of Math., ser. 2, 24(1921), 109–120.

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© 1974 Springer-Verlag

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Benzinger, H.E. (1974). An application of the hausdorff-young inequality to eigenfunction expansions. In: Sleeman, B.D., Michael, I.M. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065510

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  • DOI: https://doi.org/10.1007/BFb0065510

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06959-1

  • Online ISBN: 978-3-540-37264-6

  • eBook Packages: Springer Book Archive