Journal article
Shorter Notes: On the Mean Value of a Weakly Almost Periodic Function
Proceedings of the American Mathematical Society, v 36(1), pp 315-316
01 Nov 1972
Abstract
Let M denote the invariant mean on the space W(G) of weakly almost periodic functions on a LCA group G. The purpose of this note is to show that, for each φ ∈ W(G), \begin{equation*}\tag{1} M(\phi) = \lim_{V \rightarrow \{1 \}} \int_G \hat f_V(x) \phi (x) dx\end{equation*} where$\{V \}$is the system of compact neighborhoods of 1 in the character group Γ, and, for each V, fVis a continuous positive definite function supported in V and satisfying fV(1) = 1. This answers affirmatively a question recently raised by R. Burckel.
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Details
- Title
- Shorter Notes: On the Mean Value of a Weakly Almost Periodic Function
- Creators
- L. N. Argabright
- Publication Details
- Proceedings of the American Mathematical Society, v 36(1), pp 315-316
- Publisher
- American Mathematical Society
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:A1972O424300061
- Other Identifier
- 991021862414304721