具有常首项系数的一阶交换微分算子的象
Images of Commuting Differential Operators of Order One with Constant Leading Coefficients
摘要：
首先研究了常首项系数的一阶多项式代数的交换微分算子的象的一些性质。然后，我们提出了我们称之为关于这些微分算子的象猜想，并证明了常系数微分算子的雅可比猜想[BCW]，[E]，[Bo]（因此也是Dixobian猜想[D]）和消失猜想[Z3]实际上等价于象猜想的某些特殊情况。连接的图像猜想，因此也雅可比猜想，与多维拉普拉斯变换的多项式进行了讨论。
英文摘要：
We first study some properties of images of commuting differential operators of polynomial algebras of order one with constant leading coefficients. We then propose what we call the image conjecture on these differential operators and show that the Jacobian conjecture [BCW], [E], [Bo] (hence also the Dixmier conjecture [D]) and the vanishing conjecture [Z3] of differential operators with constant coefficients are actually equivalent to certain special cases of the image conjecture. A connection of the image conjecture, and hence also the Jacobian conjecture, with multidimensional Laplace transformations of polynomials is also discussed.
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