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On the Dirichlet Kernels with Respect to Certain Special Representative Product Systems

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The Fourier analysis uses the calculations with kernel functions from the very beginning. The maximal values of the n th Dirichlet kernels divided by n for the Walsh–Paley, “classical” Vilenkin, and some other systems are 1. In the paper, we deal with some more general systems and use the accumulated results to develop the methods aimed at determination of the properties of specific systems. In these cases, the situation with \( \frac{D_n}{n} \) may be different.

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References

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    I. Blahota, “On the maximal value of Dirichlet and Fejér kernels with respect to the Vilenkin-like space,” Publ. Math. Debrecen., 80, No. 3, 4, 503–513 (2012).

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    R. Toledo, “On the maximal value of Dirichlet kernels with respect to representative product systems,” Rend. Circ. Mat. Palermo. Ser. II, No. 82, 431–447 (2010).

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Author information

Correspondence to I. Blahota.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 11, pp. 1578–1584, November, 2014.

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Blahota, I. On the Dirichlet Kernels with Respect to Certain Special Representative Product Systems. Ukr Math J 66, 1773–1780 (2015). https://doi.org/10.1007/s11253-015-1050-z

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Keywords

  • Complete Product
  • Coordinate Function
  • Irreducible Unitary Representation
  • Dual Object
  • Dirichlet Kernel