Abstract
We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a "tame" restriction to the characteristic (hyper)surface {x(0) + x(n)p = 0} in (1 + n)-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space S'(partial derivative)_ (R-n) which we have introduced in (Ullrich in J. Math. Phys. ...
Abstract
We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a "tame" restriction to the characteristic (hyper)surface {x(0) + x(n)p = 0} in (1 + n)-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space S'(partial derivative)_ (R-n) which we have introduced in (Ullrich in J. Math. Phys. 45, 2004). Moreover, we show that every element of S'(partial derivative)_ (R-n) appears as the "tame" restriction of a solution of the (homogeneous) Klein-Gordon equation.
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