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Applicable Analysis
An International Journal
Volume 83, 2004 - Issue 7
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Original Articles

Approximate real inversion formulas of the gaussian convolution

Pages 727-733 | Received 06 Jul 2003, Accepted 05 Sep 2003, Published online: 15 Aug 2006
 

Abstract

We shall give very and surprisingly simple approximate real inversion formulas of the Gaussian convolution (the Weierstrass transform) for the first-order Sobolev Hilbert space on the whole real line by using best approximations and the theory of reproducing kernels and by using a good connection with the Tikhonov regularization.

Acknowledgement

The author wishes to express his deep thanks to Professor Masaru Ikehata for valuable discussions on the Tikhonov regularization.

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