Applied Mathematics & Information Sciences

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We prove a general form of the equiconvergence theorem using the method of V. A. Il’n. Horva ́th, Joo ́ and Komornik which provides a general theorem for the one dimensional Schro ̈ dinger operator. We prove that the theorem for certain situation is more general than the previous theorem. In particular, we write down the difference of the trigonometric kernel of the general expansion and estimate the resulting infinite sums. For the terms of these sums we used different and sharper estimates than in the previous investigations.

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