20170705Distributions in Spaces with Thick Point
摘要：The theory of distributions were introduced by Sergei Sobolev and Laurent Schwartz independently in the early 20th century. It is useful in many areas in mathematics, ranging from PDE to number theory. Modern mathematics and physics research suggest a need to consider singularities in the test function space. The theory of thick distributions in dimension one was initially introduced to deal with the occurrence of a distributional singularity on the boundary of a domain of integration. We introduced a similar theory in higher dimensions , yet the approach was quite different: we considered asymptotic expansions of test functions. I will explain the motivations of our work. I will present the construction of the new spaces, I will present several important examples of thick distributions, including the “thick delta functions". Asymptotic expansions of thick distributions will also be mentioned. In the end I will briefly discuss future research directions and how the space of thick distributions could shed light on different research areas. This is a joint work with my thesis advisor Ricardo Estrada.