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In this work we substantiate the applying of the Helmholtz vectordecomposition theorem (H-theorem) to vector fields in classicalelectrodynamics. Using the H-theorem, within the framework of the two-parameterLorentz-like gauge (so called v-gauge), we show that two kinds of magneticvector potentials exist: one of them (solenoidal) can act exclusively with thevelocity of light c and the other one (irrotational) with an arbitrary finitevelocity $v$ (including a velocity more than c . We show also that theirrotational component of the electric field has a physical meaning and canpropagate exclusively instantaneously.Comment: This variant has been accepted for publication in Found. Phys.  Letter

Helmholtz Theorem and the V-Gauge in the Problem of Superluminal and Instantaneous Signals in Classical Electrodynamics