非阿基米德伪微分算子与Feller半群
Non-Archimedean pseudodifferential operators and Feller Semigroups
摘要：
本文研究了一类符号为负定函数的非阿基米德伪微分算子。我们证明了这些算子推广到Feller半群的生成元。为了研究这些算子，我们引入了一类新的各向异性的索伯列夫空间，这是这里考虑的算子的自然域。我们还研究了某些拟微分方程的Cauchy问题。
英文摘要：
In this article we study a class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions. We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we introduce a new class of anisotropic Sobolev spaces, which are the natural domains for the operators considered here. We also study the Cauchy problem for certain pseudodifferential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
