A SIMPLE OBSERVATION ABOUT COMPACTNESS AND FAST DECAY OF FOURIER COEFFICIENTS

作者：Almira J M^*

来源：Annals of Functional Analysis, 2010, 1(1): 41-43.

DOI：10.15352/afa/1399900991

• Fourier coefficient
• frame coefficient
• continuous linear functional
• compactness in Banach spaces

Let X be a Banach space and suppose Y subset of 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 {epsilon(n)} SE arrow 0 such that vertical bar a(n)(y)vertical bar <= epsilon(n) parallel to y parallel to(Y) for every n is an element of N and every y is an element of Y. We prove this result and we use it for the study of fast decay of Fourier coefficients in L-p(T) and frame coefficients in the Hilbert setting.

• 出版日期2010