Hilbert transforms in yukawan potential theory.

Abstract:

:If H denotes the classical Hilbert transform and Hu(x) = v(x), then the functions u(x) and v(x) are the values on the real axis of a pair of conjugate functions, harmonic in the upper half-plane. This note gives a generalization of the above concepts in which the Laplace equation Deltau = 0 is replaced by the Yukawa equation Deltau = mu(2)u and in which the Cauchy-Riemann equations have a corresponding generalization. This leads to a generalized Hilbert transform H(mu). The kernel function of this new transform is expressable in terms of the Bessel function K(0). The transform is of convolution type.

authors

Duffin RJ

doi

10.1073/pnas.69.12.3677

subject

Has Abstract

pub_date

1972-12-01 00:00:00

pages

3677-9

issue

12

eissn

0027-8424

issn

1091-6490

journal_volume

69

pub_type

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