Fourier transform in bounded domains (Q1374140)

The author maintains that the concept of Schwartz distributions and their extension to ultra distributions of Gelfand and Shilov, enable one to find, by means of the Fourier transform, a second `language' to characterize physical behaviour. The author also maintains that almost any expression with physical meaning, can be transformed even if it is formulated in domains with complicated boundaries and even if it is not integrable. It is also stated that numerical procedures in the transformed space can be developed in analogy to those well-known in engineering mechanics like the methods of finite or boundary elements. In addition, the author maintains that the concept of the characteristic distribution leads to a very simple derivation of the Green-Gauss formulas for the boundary or finite elements [\textit{L. Hörmander}, ``The analysis of linear partial differential operators'', Vol. I--IV, Berlin, Heidelberg (1983; Zbl 0521.35001, Zbl 0521.35002) and (1985; Zbl 0601.35001, Zbl 0612.35011)].