AN APPROXIMATION FORMULA IN HILBERT SPACE

摘要

Let {Φk}_1~∞ be a frame for Hilbert space H. The purpose of this paper is to present an approximation formula of any f ∈ H by a linear combination of finitely many frame elements in the frame {Φk}_1~∞ and show that the obtained approximation error depends on the bounds of frame and the convergence rate of frame coefficients of f as well as the relation among frame elements.