Artículos con la etiqueta ‘Functional Analysis (math.FA)’

Set theory and topology. An introduction to the foundations of analysis. Part II: Topology – Fundamental notions

Por • 4 jul, 2013 • Category: Opinion

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as well as their applications to real numbers. Various methods to construct topological spaces are presented.

Heisenberg’s uncertainty principle in the sense of Beurling

Por • 8 jun, 2012 • Category: Opinion

We shed new light on Heisenberg’s uncertainty principle in the sense of Beurling, by offering an essentially different proof which permits us to weaken the assumptions substantially, and examples show that the result is sharp. The proof involves Fourier and Mellin transforms. We alo extend to a setting of two functions. A higher-dimensional analogue is considered as well.