Lp-convergence for expansions in terms of the eigenfunctions of a Sturm — Liouville problem |
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Authors: | V L Generozov |
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Institution: | (1) M. V. Lomonosov Moscow State University, USSR |
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Abstract: | For the operator Lv=–(x2ay ) . x 0, 1], y(0)=y(1)=0 with 0 ![le](/content/j7808163083n7312/xxlarge8804.gif) < 1/2, or ¦y¦ < , y(1)=0 with 1/2![le](/content/j7808163083n7312/xxlarge8804.gif) <1, we investigate the effect which the singularity of the Sturm-Liouville operator derived from this self-adjoint expression has on Lp-convergence of expansions in terms of the eigenfunctions of this operator. We will prove that the orthonormalized system of eigenfunctions forms a basis in Lp 0, 1] for 2/(2– ) < p < 2/ .Translated from Matematicheskii Zametki, Vol. 3, No. 6, pp. 683–692, June, 1968.The author is grateful to V. M. Tikhomirov for his many valuable remarks and his constant attention to this work. |
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