On a Generalization of Hilbert Transform

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概要

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• Hilbert Transform is generalized based on the assumption of the complex analytic functions only in the strict upper-half plane Imz>0,insted of the usual assumption in Imz≧0. Our method gives the mathematical basis of the regularization of some singular integrals and also gives a new viewpoint of distribution theory and hyperfunction theory. Our viewpoint is excelent because it is easy to understand and is explicit in presentation : we do not use the concept of "the test function", "the inductive limit" and "the defining function". The mathematical connection with two dimensional potential-theory is also given. It is interesting to apply our result to the global theory of the electric heart pulse of biologycal systems.

• 八戸工業大学の論文
• 1994-03-31

著者

• Ohkuro Shigeru

  Hachinohe Institute Of Technology

関連論文

• On a Generalization of Hilbert Transform
• The Symmetry of Imaginary Unit and the Regularization of Integrals

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