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Coincidence criteria for the kernel of a function and the kernel of its integral almost positive means

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Abstract

We establish necessary and sufficient conditions for a point A of the Knopp kernelK(f) of a functionf to belong to the kernelK(M) of a functionM(t):=∫ S fdμ t , where the so-called almost positive measures μ t determine a regular method of summation. In particular, this gives coincidence criteria for the kernelsK(f) andK(M).

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Authors
  1. E. G. Usenko
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Additional information

National Pedagogical University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 9, pp. 1267–1275, September, 1999.

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Usenko, E.G. Coincidence criteria for the kernel of a function and the kernel of its integral almost positive means. Ukr Math J 51, 1425–1434 (1999). https://doi.org/10.1007/BF02593008

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  • DOI: https://doi.org/10.1007/BF02593008

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