关于 Dirichlet 空间核函数的说明

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2024-09-23 DOI:10.1016/j.jmaa.2024.128897

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引用次数: 0

摘要

对于平面域 Ω，我们考虑关于基点 ζ∈Ω 的 Dirichlet 空间和相应的核函数。我们还不知道这些核函数在我们改变基点时是如何表现的。在本说明中，我们将证明这些核函数的变化是平滑的。作为平滑性结果的应用，我们证明了这些核函数在 Ω×Ω 上的拉马丹诺夫型定理。这扩展了之前已知的这些核函数的收敛结果。事实上，我们是在更一般的情况下，即针对加权核函数及其高阶对应函数，得出这些结论的。

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A note on kernel functions of Dirichlet spaces

For a planar domain Ω, we consider the Dirichlet spaces with respect to a base point

ζ \in Ω

and the corresponding kernel functions. It is not known how these kernel functions behave as we vary the base point. In this note, we prove that these kernel functions vary smoothly. As an application of the smoothness result, we prove a Ramadanov-type theorem for these kernel functions on

Ω \times Ω

. This extends the previously known convergence results of these kernel functions. In fact, we have made these observations in a more general setting, that is, for weighted kernel functions and their higher-order counterparts.

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来源期刊

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.