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Are the Fourier transform non-radiation conditions of Pearle and Haus identical?

Philip Pearle published in chapter 7 Classical Electron Models of the 1982 book Electromagnetism edited by Doris Teplitz, a Fourier Transform approach to Goedecke's earlier non-radiation condition culminating in equation (6.16): enter image description here This appears to originate with Pearle (there being no cite).

Then in 1986, H. A. Haus in "On the radiation from point charges" (Am. J. Phys. 54 (12)) we have equation (13) providing another approach to the non-radiation condition using the Fourier Transform: enter image description here enter image description here

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