The problem of inversion the integral Laplace transform, which belongs to class ill-posed problems, is considered. Integral equations are reduced ill-conditioned systems linear algebraic equations, in unknowns either coefficients series expansion terms special functions, or approximate values desired original at a number points. Described method using quadrature formulas highest degree accuracy...

We introduce a generalization of the Fourier transform, denoted by FC , on the isotropic cone C associated to an indefinite quadratic form of signature (n1, n2) on R (n = n1 + n2: even). This transform is in some sense the unique and natural unitary operator on L2(C), as is the case with the Euclidean Fourier transform FRn on L 2(Rn). Inspired by recent developments of algebraic representation ...

Noises are usually assumed to be Gaussian so that many existing signal processing techniques can be applied with no worry. However, in many real world natural or man-made systems, noises are usually heavy-tailed. It is increasingly desirable to address the problem of finding an opportune filter function for a given input noise in order to generate a desired output noise. By filtering theory, th...