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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

11 votes
0 answers
598 views

High-dimensional geometry: Top-down Vs. Bottom-up

There are several ways to leverage one's intuition from low-dimensional geometry to understand high-dimensional phenomena. For example, one can get a clearer picture of the behaviour of high-dimension …
Simon Lyons's user avatar
  • 1,666
7 votes
2 answers
613 views

Is there a tropical analogue of a reproducing kernel Hilbert space?

In classical functional analysis, one can construct a reproducing kernel Hilbert space by starting with a positive definite kernel, say $K: [0,1]\times [0,1] \rightarrow \mathbb{R}$. One then creates …
Simon Lyons's user avatar
  • 1,666