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Determination of jumps in terms of derivative convolution operators

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Abstract

X. L. Shi and W. Wang [12] studied the question on determination of jumps for functions via conjugate convolution operators. In the present paper a different way to calculate jumps is discussed. We show that derivative convolution operators can be used to determine jumps for functions. Furthurmore, we point out that the assumption “ϕ is even” in Shi–Wang’s theorem can be removed.

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Authors and Affiliations

  1. College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), Hunan Normal University, Changsha, Hunan, 410081, P. R. China

    Y. Chen & X. L. Shi

Authors
  1. Y. Chen
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  2. X. L. Shi
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Correspondence to X. L. Shi.

Additional information

Project 11071065 and Project 11171306 supported by NSF of China. Project 20094306110004 supported by Ph. D. Programs Foundation of the Ministry of Education of China. Supported by Program for Science and Technology Research in Higher Educational Institutions of Hunan Province of China.

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Chen, Y., Shi, X.L. Determination of jumps in terms of derivative convolution operators. Acta Math Hung 139, 372–392 (2013). https://doi.org/10.1007/s10474-012-0268-6

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  • DOI: https://doi.org/10.1007/s10474-012-0268-6

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