image-approximation to Laplace transforms of signed measures Original Research Article

For functions that are piecewise equal to one-sided Laplace transforms of signed measures, we construct interpolations that are entire functions with interpolation points that are zeros of Laguerre–Pólya entire functions. If the interpolated function image is sufficiently regular, these interpolations are best approximations in image-norm to image by functions of fixed exponential type. This is demonstrated for the example image with image.