Fourier Analysis of Semistable Distributions

Distributions and Fourier Transform

Introduction. The theory of distributions, or generalized functions, provides a unified framework for performing standard calculus operations on nonsmooth functions, measures (such as the Dirac delta function), and even more general measure-like objects in the same way as they are done for smooth functions. In this theory, any distribution can be differentiated arbitrarily many times, a large c...

Generalized Fourier Transforms of Distributions

In [1], R. A. Kunze has presented a notion of generalized Fourier transform of functions on locally compact abelian groups. The point of this paper is to extend this idea in the direction of distribution theory and to present some initial results on this generalized Fourier transform of distributions. In a later paper we hope to investigate in detail the domain, range, and kernel of this transf...

Fourier-Based Testing for Families of Distributions

We study the general problem of testing whether an unknown discrete distribution belongs to a given family of distributions. More specifically, given a class of distributions P and sample access to an unknown distribution P, we want to distinguish (with high probability) between the case that P ∈ P and the case that P is ǫ-far, in total variation distance, from every distribution in P . This is...

Of Semistable Galois

Meshless analysis of casting process considering non-Fourier heat transfer

Casting is considered as a major manufacturing process. Thermal analysis of a solidifying medium is of great importance for appropriate design of casting processes. The conventional governing equation of a solidifying medium is based on the Fourier heat conduction law, which does not account for the phase-lag between the heat flux and the temperature gradient. In this paper, the concept of phas...