关键词: frame, continuous frame, measurable space, Riesz basis, excess

Abstract: The discrete frame and the continuous frame in a Hilbert space are discussed. By the tool excess of a sequence, a sufficient and necessary condition is presented under which a discrete frame is equivalent to a continuous frame with respect to the whole natural numbers with a positive Borel measure. And some examples are given to illuminate the condition.

Key words: frame, continuous frame, measurable space, Riesz basis, excess