论文标题
一些措施和高斯半群的抛物线方程
Some parabolic equations for measures and Gaussian semigroups
论文作者
论文摘要
这种简短的交流（预印本）致力于对数学物理学和量子理论很重要的进化方程的数学研究。我们为这些方程式解决方案提供了新的显式公式，并讨论了它们的属性。结果是没有证据的，但是证据将出现在现在正在准备的较长文本中。 在本文中，在措施类别中考虑了schrödinger方程的欧几里德类似物的无限维概括。这些方程式的库奇问题得到了解决。在特定情况下，获得了基本解决方案的显式公式，这是Mehler公式的概括，并且证明了解决方案的独特性。构建了Ornstein-Uhlenbeck度量的类似物。给出了高斯半群的定义，并描述了它们与所考虑的抛物线方程的联系。
This short communication (preprint) is devoted to mathematical study of evolution equations that are important for mathematical physics and quantum theory; we present new explicit formulas for solutions of these equations and discuss their properties. The results are given without proofs but the proofs will appear in the longer text which is now under preparation. In this paper, infinite-dimensional generalizations of the Euclidean analogue of the Schrödinger equation for anharmonic oscillator are considered in the class of measures. The Cauchy problem for these equations is solved. In particular cases, explicit formulas for fundamental solutions are obtained, which are a generalization of the Mehler formula, and the uniqueness of the solution with certain properties is proved. An analogue of the Ornstein-Uhlenbeck measure is constructed. The definition of Gaussian semigroups is given and their connection with the considered parabolic equations is described.
