Laplace Transforms of Hyperfunctions: Another Foundation of the Heaviside Operational Calculus
Laplace Transforms of Hyperfunctions: Another Foundation of the Heaviside Operational Calculus
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超函数的拉普拉斯变换：亥维赛运算微积分的另一个基础
DOI：
10.1007/978-1-4613-1055-6_5
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发表时间：
1988
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通讯作者：
H. Komatsu
中科院分区：
文献类型：
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作者：
H. Komatsu
首先，我们将利用格林公式(d/dx)i(e(X)u(X)=e(X)u(I)(X)+o(X)u(Il)(O)+··+o(Il)(X)u(O)，(7)i，其中u e：C(IR)和e(X)是Heaviside函数)，将初值问题(4)化为一个更简单的分布问题。也就是说，如果我们考虑分布e(X)f(X)和e(X)u(X)而不是函数f和u，则问题(4)等价于分布u e的以下问题：在[0，00)中支持的IR上的0[0，00)：给定f e：v[O，oo)‘找到解u e：0[0，00)使得
First, we shall reduce the initial value problem (4) to a simpler problem for distributions by employing the Green formula (d/dx) i (e (x) u (x»= e (x) u (i)(x)+ o (x) u (il)(O)+••.+ o (il)(x) u (O),(7) i where u e: C (IR) and e (x) is the Heaviside function. Namely, if we consider the distributions e (x) f (x) and e (x) u (x) instead of the functions f and u, the problem (4) becomes equivalent to the following problem for distributions u e: 0 [0, 00) on IR with support in [0, 00): Given an f e: V [O, oo)'find a solution u e: 0 [0, 00) such that