Strong Cesàro summability of triple Fourier integrals
2014
scientific article
english
- triple Fourier transform and integral
- inversion formula
- partial (or Dirichlet) integral
- (C‚ 1) summability and strong q - Cesàro summability
EN The theory of summability is a very extensive field, which has various applications. We prove the following theorem. Assume ƒ ϵ L∞(R3) with bounded support. If ƒ is continuous at some point (x1, x2, x3) ϵ R3, then the triple Fourier integral of ƒ is strongly q-Cesàro summable at (x1, x2, x3) to the function value ƒ (x1, x2, x3) for every 0 < q < ∞. Furthermore, if ƒ is continuous on some open subset G of R3, then the strong q-Cesàro summability of the triple Fourier integral of ƒ is locally uniform on G.
95 - 112
CC BY-NC-ND (attribution - noncommercial - no derivatives)
public
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