Approximating signals in the abstract

作者：Dodson M M^*

来源：Applicable Analysis, 2011, 90(3-4): 563-578.

DOI：10.1080/00036811003627575

• locally compact abelian groups
• abstract harmonic analysis
• sampling theory
• an approximate Kluvanek theorem

An analogue of the classical approximate sampling theorem is proved for the abstract analogue of a signal, i.e. a function on a locally compact abelian group that is continuous, square-integrable with an integrable Fourier-Plancherel transform. An additional hypothesis that the samples of the function are square-summable is needed and is discussed. This hypothesis is not very restrictive as in a sense it 'almost always' holds. Two asymptotic formulae are also obtained under some further conditions on the group.

• 出版日期2011