【摘要】 讨论两类偏微分算子的非解析亚椭圆性 ,所用方法是直接构造这些算子的奇异解后 ,将问题转化成对某些特殊的常微分方程的讨论。该构造过程是非常清晰和直接的 ,而且它涉及到那些带有依赖大参数位势的广义调和振子的第一特征值和第一特征函数的研究。更多还原

【Abstract】 The non analytic hypoellipticity of two class partial differential operators is discussed . By the method of constructing singular solutions of these operators,the discussion is transformed to a study of some special ordinary differential equations. This construction is quite explicit and it is involved into the study of the first eigenvalue and the first eigenfunction of a generalized harmonic oscillator with a potential depending on a large parameter.更多还原