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The results (1)-(2) are proved in the present research work. (1) The estimation for the solution of the Schrödinger operator in a closed domain. (2) Problem of uniform convergence of spectral expansions connected with Schrödinger operator of continuous functions in a closed domain. The summability and spectral expansions of the first boundary value problem for Schrödinger operator in closed domain are discussed. The representations used in this research work allow the methods given in [20] and [28] for the spectral expansion and summability of Schrödinger operator in a closed domain. The new estimation and summability connected with one of the Schrödinger operator in a closed domain are derived.
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