arXiv subjects

Garving K. Luli

Publications and source records attributed to Garving K. Luli.

21 records · Page 2Linked to original sources

arXiv2012

The Structure of Sobolev Extension Operators

Let $L^{m,p}(\R^n)$ denote the Sobolev space of functions whose $m$-th derivatives lie in $L^p(\R^n)$, and assume that $p>n$. For $E \subset \R^n$, denote by $L^{m,p}(E)$ the space of restrictions to $E$ of functions $F \in L^{m,p}(\R^n)$. It is known that there exist bounded linear maps $T : L^{m,p}(E) \rightarrow L^{m,p}(\R^n)$ such that $Tf = f$ on $E$ for any $f \in L^{m,p}(E)$. We show that $T$ cannot have a simple form called "bounded depth."

math.CA↗

arXiv2012

The Brenner-Hochster-Kollár and Whitney Problems for Vector-valued Functions and Jets

In this paper, we give analytic methods for finding m (and m+ω) times continuously differentiable solutions of a finite system of linear equations. Along the way, we also solve a generalized Whitney problem for vector-valued functions and jets.

math.AG↗

arXiv2012

Sobolev Extension By Linear Operators

Let $L^{m,p}(\R^n)$ be the Sobolev space of functions with $m^{th}$ derivatives lying in $L^p(\R^n)$. Assume that $n< p < \infty$. For $E \subset \R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in $L^{m,p}(\R^n)$. We show that there exists a bounded linear map $T : L^{m,p}(E) \rightarrow L^{m,p}(\R^n)$ such that, for any $f \in L^{m,p}(E)$, we have $Tf = f$ on $E$. We also give a formula for the order of magnitude of $\|f\|_{L^{m,p}(E)}$ for a given $f : E \rightarrow \R$ when $E$ is finite.

math.CA↗