The Image Space of One Type of Continuous Wavelet Transform and its Property

In this paper, we show that the space of continuous wavelet transform is a reproducing kernel Hilbert space based on the fundamental theorem of linear transform. An admissible wavelet is got by convolution computation which is made into continuous wavelet transform. By the theory of reproducing kernel we can discuss correlative properties of image space of wavelet transform, which provide theoretic frame for us to study image space of the general wavelet transform.

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