Compact pseudodifferential operators whose symbol fails to be smooth with respect to x on a given set are considered. Conditions under which Weyl’s law of spectral asymptotics remains valid for such operators are obtained. The results are applied to operators with symbols such that their order of decay as |ξ| → ∞ is a nonsmooth function of x.

中文翻译：

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空间变量中符号非光滑的紧致伪微分算子的奇异数的渐近行为

考虑其符号相对于给定集合上的x不能平滑的紧凑型伪微分算符。获得了这样的条件，在该条件下，魏尔谱渐近定律对于此类算子仍然有效。将结果应用于带符号的算子，使其衰减顺序为||||。→∞是x的非光滑函数。