We investigate the association of compactness and coefficients of linear combinations of composition operators acting on bounded holomorphic function space H~∞(B_N) in the unit ball of C~N.The paper is mainly divided into there chapters.The first section is the introduction of the whole paper.Which includes the background, and the main results are given here too.Next section of the paper,some important definitions and lemmas,which are related to the main theorems.The third part are the proofs of the main theorems and corollaries.
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