Zur Struktur 1‐planarer Graphen
Zur Struktur 1‐planarer Graphen
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DOI：
10.1002/mana.19861250122
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发表时间：
1986
影响因子：
1
通讯作者：
Von H. Schumacher
中科院分区：
文献类型：
--
作者：
Von H. Schumacher
众所周知，对于常系数微分算子的CAUCHY问题，当初始超平面为特征且对其解不加任何限制时，CAUCHY问题没有唯一解[5]，[lo]。L. H~ R-MANDER证明了特征CAUCHY问题[4]，[5]解存在的充分必要条件。本文寻找了一类在一定方向上被调质的分布的解，并给出了任意常系数微分算子的特征CAUCHY问题在这类上的唯一性的充分必要条件。还建立了与非唯一性remts的连接。设P （D,, 0,）为任意常系数微分算子，其超平面t= const为特征。ln = R, x€Rn, Dzj=-
It is well known that the CAUCHY problem for differential operators with constant coefficients has no unique solution when the initial hyperplane is characteristic and no restrictions on the solutions are imposed [5],[lo]. L. H~ R-MANDER has proved necessary and sufficient conditions for existence of solutions to the characteristic CAUCHY problems [4],[5]. In this paper one looks for solutions in a class of distributions which are tempered in certain directions and a necessary and sufficient condition for uniqueness in this class of the characteristic CAUCHY problems for arbitrary differential operators with constant coefficients is given. A connection with the non-uniqueness remlts is also established. Let P (D,, 0,) be an arbitrary differential operator with constant coefficients, for which the hyperplanes t= const are characteristic. la t E R, x€ Rn, Dzj=-