Linearization Techniques for Holomorphic Functions and Lipschitz-Free Spaces (22rit001)

Organizers

(Kent State University)

Veronica Dimant (Universidad de San Andrés)

Let $\mathcal S(U;Y)$ be a set of continuous functions, defined on an open subset $U$ of a Banach space $X,$ taking values in a Banach space $Y.$ In order to study this set, one natural technique is to {\em linearize} the functions in $\mathcal S(U;Y)$ by finding a new space $Z$ and a natural mapping $\iota:U \to Z$ such that each $f \in \mathcal S(U;Y)$ corresponds to a continuous linear operator $T_f:Z \to Y$ satisfying $f = T_f \circ \iota,$ and conversely. The result is that the (possibly) unwieldy function $f$ is replaced by a linear operator $T_f$ which (possibly) is acting on a much larger, unwieldy space $Z.$ Perhaps surprisingly, this technique often yields interesting, new results.