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Criteria for the coincidence of the kernel of a function with the kernels of its Riesz and Abel integral means

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Abstract

We indicate criteria for the coincidence of the Knopp kernels K(f) K(A f), and K (R f) of bounded functions f(t); here,

$$R_f \left( t \right) = \frac{1}{{P\left( x \right)}}\int\limits_{\left[ {0;\left. t \right)} \right.} {f\left( x \right)dP and A_f \left( t \right)} = \frac{1}{{\int_0^\infty {e^{{{ - x} \mathord{\left/ {\vphantom {{ - x} t}} \right. \kern-\nulldelimiterspace} t}} dP} }}\int\limits_0^\infty {f\left( x \right)} e^{{{ - x} \mathord{\left/ {\vphantom {{ - x} t}} \right. \kern-\nulldelimiterspace} t}} dP$$

. In Particular, we prove that K(f) = K(A f) ⇔ K(f) = K(R f).

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References

  1. A. V. Revenko, “Imbedding of kernels by regular transformations,” Ukr. Mat. Zh., 36, No. 5, 662–666 (1984).

    MathSciNet  Google Scholar 

  2. N. Bourbaki, Espaces Vectoriels Topologiques, Hermann, Paris.

  3. N. A. Davydov and G. A. Mikhalin, “On the kernels of bounded sequences,” Mat. Zametki, 23, No. 4, 537–550 (1978).

    MATH  MathSciNet  Google Scholar 

  4. G. A. Mikhalin, “Conditions for coincidence of the kernel of a sequence with the kernels of its (R, p n, α) and (J, p n) means,” Ukr. Mat. Zh., 31, No. 51, 504–509 (1979).

    MATH  MathSciNet  Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 12, pp. 1712–1714, December, 1998.

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Usenko, E.G. Criteria for the coincidence of the kernel of a function with the kernels of its Riesz and Abel integral means. Ukr Math J 50, 1952–1955 (1998). https://doi.org/10.1007/BF02514212

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  • DOI: https://doi.org/10.1007/BF02514212

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