Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Extension of vector-valued functions and weak-strong principles for differentiable functions of finite order (1910.01952v5)

Published 4 Oct 2019 in math.FA

Abstract: In this paper we study the problem of extending functions with values in a locally convex Hausdorff space $E$ over a field $\mathbb{K}$, which have weak extensions in a weighted Banach space $\mathcal{F}\nu(\Omega,\mathbb{K})$ of scalar-valued functions on a set $\Omega$, to functions in a vector-valued counterpart $\mathcal{F}\nu(\Omega,E)$ of $\mathcal{F}\nu(\Omega,\mathbb{K})$. Our findings rely on a description of vector-valued functions as linear continuous operators and extend results of Frerick, Jord\'{a} and Wengenroth. As an application we derive weak-strong principles for continuously partially differentiable functions of finite order, vector-valued versions of Blaschke's convergence theorem for several spaces and Wolff type descriptions of dual spaces.

Summary

We haven't generated a summary for this paper yet.