Abstract
Differential operatorsp(t, ∂)=a m (t)∂ m +···+a 0(t), wherea m has a zero of finite order att=0, are studied as operators on the distribution spacesD'(R) andE'(R). In particular the kernel ofp, operating onD'(R), is studied in detail by use of asymptotic analysis and a simple formula for its dimension is given. A continuous right inverse forp onD'(R) is constructed. Necessary and sufficient conditions for this inverse to be two-sided are given. Extensions are made to the spacesE (R) andE'(R). Finally some features for operators with more than one singular point are briefly discussed and there is noted a phenomenon — forced propagation of supports — which has important consequences in higher dimensions as a forced propagation of singularities.
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Svensson, S.L. Singular differential operators and distributions. Israel J. Math. 38, 131–153 (1981). https://doi.org/10.1007/BF02761856
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DOI: https://doi.org/10.1007/BF02761856