Laplace Transform of Distribution-valued Functions and Its Applications
نویسندگان
چکیده
1. Notation and notions We repeat some definitions and facts, we need in our exposition but for special case. Let Q be an open set belonging to Rn. By D(Q) we denote the space {φ ∈ C∞(Q); suppφ ⊂ Kφ}, Kφ is a compact set in Q which depends on φ. D′(Q) is the space of continuous linear functionals on D(Q) the space of distributions. Every f ∈ Lloc(Q) defines a distribution, called regular distribution, denoted by [f ], 〈[f ], φ〉 = ∫ Q f(t)φ(t)dt, φ ∈ D(Q).
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