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Bracket Products on Locally Compact Abelian Groups

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We define a new function-valued inner product on L2(G), called ِ-bracket product, where G is a locally compact abelian group and partial is a topological isomorphism on G. We investigate the notion of -partial orthogonality, Besselיs Inequality and partial-orthonormal bases with respect to this inner product on L2(G).

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