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


(Kent State University)

Veronica Dimant (Universidad de San Andrés)

(Universidad de Valencia)

Luis C. García-Lirola (Universidad de Zaragoza)


The Banff International Research Station will host the "Linearization Techniques for Holomorphic Functions and Lipschitz-Free Spaces" workshop in Banff from July 24, 2022 to August 7, 2022.

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.

The origin of this proposal is that two different groups of researchers have realized that they were using the same general process of linearization, one in the complex setting to linearize many spaces of holomorphic mappings, and the other in the real setting in the study of spaces of Lipschitz functions to build the Lipschitz-free spaces. We are convinced that the deep analysis and joint research that would be done at BIRS should produce relevant advances in both fields of research.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT).