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Regularization of a Distribution Holomorphic in a Parameter
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2023-11-24 , DOI: 10.1134/s0037446623060137 A. L. Pavlov
中文翻译:
参数分布全纯的正则化
更新日期:2023-11-24
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2023-11-24 , DOI: 10.1134/s0037446623060137 A. L. Pavlov
We give sufficient conditions for regularizing a distribution of the form \( a(\sigma,\lambda)f(\lambda) \), where \( f(\lambda) \) is a distribution holomorphic in the parameter \( \lambda \), while \( a(\sigma,\lambda) \) is an infinitely differentiable function of \( \sigma \) outside some closed set \( N \) with power singularities of derivatives on \( N \) and holomorphic in \( \lambda \).
中文翻译:
参数分布全纯的正则化
我们给出了正则化形式为 \( a(\sigma,\lambda)f(\lambda) \) 的分布的充分条件,其中 \( f(\lambda) \) 是参数 \( \lambda中的全纯分布\),而 \( a(\sigma,\lambda) \)是\( \sigma \) 的无限可微函数, 在某个闭集 \( N \)之外 ,具有 \( N \)上导数的幂奇异性 和全纯在 \(\lambda \)中。