Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1203.42002
Almira, J.M.
A simple observation about compactness and fast decay of Fourier coefficients. (English)
[J] Ann. Funct. Anal. AFA 1, No. 1, 41-43, electronic only (2010). ISSN 2008-8752/e

Summary: Let $X$ be a Banach space and suppose $Y\subseteq X$ is a Banach space compactly embedded into $X$, and $(a_k)$ is a weakly null sequence of functionals in $X^*$ . Then there exists a sequence $\{\varepsilon_n\}\searrow 0$ such that $|a_n(y)|\le \varepsilon_n\|y\|_Y$ for every $n\in\Bbb N$ and every $y\in Y$. We prove this result and we use it for the study of fast decay of Fourier coefficients in $L^p(\Bbb T)$ and frame coefficients in the Hilbert setting.

MSC 2000:: *42A16 Fourier coefficients, etc.
46B50 Compactness in normed spaces

Keywords: Fourier coefficient; frame coefficient; continuous linear functional; compactness in Banach spaces

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]