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.