<!DOCTYPE html>
<html>
<head>
<title>Set Theory and Analysis</title>
</head>
<body>
<p>
Tuesday 14 May 2024 - 10:00 to 11:30 <br />
Place: IM, konírna
</p>
<p>
Speaker: Marián Fabian, IM CAS<br />
Title: Fréchet differentiability versus Gateaux differentiability - counter-examples
</p>
<p class="ql-ed">
Abstract <br />
<p>We investigate several statements from analysis, what happens if Fréchet differentiability </p><p>is replaced by Gateaux differentiability. A culminating result is an example showing non-validity of </p><p>``Gateaux'' form of chain rule: There exists an involution $f:\R<sup>^2</sup> \longrightarrow \R<sup>^2</sup>$, Gateaux differentiable at (0,0), with singular Jacobian Jf(0,0)=( 0 0 // 1 0), and hence </p><p>Jf(0,0) Jf(0,0) = (0 0 // 0 0), which is not identity matrix. </p><p><br></p><p>The statements presented come from a forthcoming joint paper of Jan Kolar and me. </p>
</p>
<p>
For more information see the seminar web page at <br />
https://www.math.cas.cz/index.php/events/seminar/6
</p>
<p>
Set Theory and Analysis mailing list <br />
settfa@math.cas.cz <br />
https://list.math.cas.cz/listinfo/settfa@math.cas.cz
</p>
</body>
</html>