由于-凸泛函的广泛性和定理形式的一般性，共鸣定理的这种形式在凸体理论等研究领域具有广泛的应用。
Owing to the generality of -convex functionals and the theorem forms, these forms of resonance theorem have wide application in such fields as convex body theory.
给出了有关凸泛函的两个命题，并由此对凸下半连续泛函的下控定理、次可微定理的条件、结论及证法进行了探讨。
As to their applications, some results about the low control theorem of the convex lower semi-continuous function and the subdifferentiable function theorem are obtained.
拓扑线性空间的局部双序凸性，是该空间上连续线性泛函实现双序正分解的基础。
The Local biorder-convexity is a base of the biordering positive decomposition of linear functionals.
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