Uniqueness in the Characteristic Cauchy Problem of the Klein-gordon Equation and Tame Restrictions of Generalized Functions
نویسنده
چکیده
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 {x0 + x = 0} in (1 + n)-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space S′ ∂ − (R) which we have introduced in [16]. Moreover, we show that every element of S′ ∂ − (R) appears as the “tame” restriction of a solution of the (homogeneous) Klein-Gordon equation.
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