tempered distribution

缓增分布

Analysis, Measure & PDE · Graduate · Mathematics Resources editorial compilation (AI-assisted)

Translation evidence: Literature usage

Meaning in context

A tempered distribution on R^n is a continuous linear functional on Schwartz space with its topology given by all polynomially weighted derivative seminorms.

缓增分布是速降函数空间上的连续线性泛函，连续性须相对于所有多项式加权导数半范数所定义的拓扑。

Example

The constant function $2$ defines $T(\varphi)=2\int\varphi$, bounded by a sufficiently weighted Schwartz seminorm.

Usage and distinctions

Continuity on compactly supported tests defines an ordinary distribution; Schwartz tests impose additional control at infinity.

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Mikko Salo — Fourier Analysis and Distribution Theory§3.2, definition of S′ and Example 3.2.1 · Checked 2026-10-14

Translation sources

1. 电子科技大学 — 泛函分析教学大纲第三章，了解5：速降函数和缓增分布 · Checked 2026-10-14

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