AN EQUICONVERGENCE THEOREM FOR LINEAR ORDINARY DIFFERENTIAL OPERATOR

M. B. Tahir and A. K. Yaseen

  DOI:  https://doi.org/10.37418/amsj.9.11.42

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The aim of the present paper is to prove a general equiconvergence theorem for ordinary linear differential operator of $3^{rd}$-order, $Lu:=u^3+q(x)u$, which extends the results of Horvath, Jo\'{o} and Komornik for the Schr\”{o}dinger operators of second order.

Keywords: Differential operators, equiconvergence, eigenfunction expansions, Schr\”{o}dinger operator, Riesz bases.