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Non-archimedean pseudo-differential operators on Sobolev spaces related to negative definite functions
Journal of Pseudo-Differential Operators and Applications ( IF 1.1 ) Pub Date : 2021-02-10 , DOI: 10.1007/s11868-021-00385-z Anselmo Torresblanca-Badillo
中文翻译:
Sobolev空间上与负定函数有关的非archivedean伪微分算子
更新日期:2021-02-10
Journal of Pseudo-Differential Operators and Applications ( IF 1.1 ) Pub Date : 2021-02-10 , DOI: 10.1007/s11868-021-00385-z Anselmo Torresblanca-Badillo
In this article we study a large class of pseudo-differential operators on Sobolev spaces related to negative definite functions in the p-adic context and in arbitrary dimension. We show that these operators are m-dissipatives and generators of a strongly continuous contraction semigroup on the sobolev spaces mentioned above. Also, we study the convolution kernel, the Green function and the heat kernel attached to these operators. In addition, we study certain inhomogeneous equations and the Cauchy problem naturally associated to these operators.
中文翻译:
Sobolev空间上与负定函数有关的非archivedean伪微分算子
在本文中,我们研究了Sobolev空间上的一类伪伪微分算子,该伪微分算子与p- adic上下文和任意维中的负定函数有关。我们证明了这些算子是上述sobolev空间上的一个强连续收缩半群的m耗散和生成器。此外,我们研究了卷积核,格林函数和与这些算子连接的热核。此外,我们研究了某些非齐次方程以及与这些算子自然相关的柯西问题。