| Thu, Apr 18, 2024
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Colloquium
3:30 PM
MSCS 514 | | Extensions with Constraints
Kevin Luli, UC Davis
| | | Abstract: Fix integers m, n. Let X be your favorite function space, e.g., $C^m(R^n)$ or Sobolev spaces. Given a closed subset E of $R^n$ and a function $f: E \to R$, how can we tell if there exists F in X such that $F|_E = f$? How about in addition to $F|_E = f$, we require $F$ to satisfy some convex constraints, for example, (nonnegativity) $F \geq 0$? If such an F exists, how small can the X-norm be? If E consists of N points, can we efficiently produce such an F? In this talk, I will address these questions along with their further generalizations to the settings of vector-valued functions F. |
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