Abstract
Two properties of the radiation emitted by a relativistic electron in an external field, in the classical approximation, are presented in details: 1) spectral sum rules and their relationship with the sum rules for oscillator strength in atomic physics. Filtered sum rules can be used to remove infrared or ultraviolet divergences. 2) "half-naked electron" effects like the Landau- Pomeranchuk-Migdal and Ternovskij-Shul'ga-Fomin effects. These properties are best understood when introducing the apparent transverse velocity.
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