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Hausdorff-Young inequality for the eigenfunctions and associated functions of a differential operator of second order

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    V. A. Il'in and I. Io, “The Bessel and the Hausdorff-Young-Riesz type inequalities for functions from the class of the functions that are radial with respect to the system of eigenfunctions of the Laplace operator,” Dokl. Akad. Nauk SSSR,291, No. 2, 284–288 (1986).

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    V. A. Il'in, “On the unconditional basicity on a closed interval of systems of the eigen-functions and associated functions of a differential operator of second order,” Dokl. Akad. Nauk SSSR,273, No. 5, 1049–1053 (1983).

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    V. A. Il'in, “On the convergence of the expansions in eigenfunctions at the points of discontinuity of the coefficients of a differential operator,” Mat. Zametki,22, No. 5, 679–698 (1977).

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    I. S. Lomov, “Certain properties of the eigenfunctions and associated functions of the Sturm-Liouville opertor,” Differents. Uravn.,18, No. 10, 1684–1694 (1982).

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Translated from Matematicheskie Zametki, Vol. 42, No. 3, pp. 411–421, September, 1987.

The author thanks V. A. Il'in for the formulation of the problem and assistance with the note and V. S. Serov for useful discussions about the results of this note.

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Karov, K.M. Hausdorff-Young inequality for the eigenfunctions and associated functions of a differential operator of second order. Mathematical Notes of the Academy of Sciences of the USSR 42, 726–732 (1987). https://doi.org/10.1007/BF01138639

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Keywords

  • Differential Operator