Maxentropic reconstruction of Fourier and Laplace transforms
The moment problem on \([0,1]\), i.e., the problem of reconstructing a continuous, positive function on [0,1] when only a few of its moments are known has received a lot of attention. In this note, the first of a series, the author presents a maxentropic procedure to recover a function from the knowledge of a finite number of values of a linear integral transform, and apply it to the case of the Fourier or the Laplace transforms. The author also considers the case in which the values of the transform are known to be polluted by the noise.
scientific article; zbMATH DE number 847553