Paley – Wiener type theorem for functions with values in Banach spaces

• Date: 2022
• Main Authors: Bang, H. H., Huy, V. N.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2382
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 Let $(\mathbb{X},\|.\|_{\mathbb{X}})$ denote a complex Banach space and $L(\mathbb{X})=BC (\mathbb{R}\to\mathbb{X})$ be the set of all $\mathbb{X}$-valued bounded continuous functions $f\colon\mathbb{R}\to\mathbb{X}.$For $f\in L(\mathbb{X})$ we define $\|f\|_{L(\mathbb{X})}=\sup\{ \|f(x)\|...