abstract harmonic analysis

uncountable

(harmonic analysis, representation theory, topology) A branch of harmonic analysis dealing with generalised Fourier transforms that act on functions defined on Hausdorff locally compact topological groups.

Japanese Meaning

抽象調和解析：ハウスドルフかつ局所コンパクトな位相群上で定義された関数に対して、一般化されたフーリエ変換を用いる調和解析の一分野。調和解析、表現論、位相数学の概念を融合し、従来の調和解析の枠組みを拡大する研究領域。

What is this buttons?

Recent breakthroughs in representation theory have deepened our understanding of abstract harmonic analysis on Hausdorff locally compact topological groups.

Google Translation / DeepL Translation

表現論の最近の進展により、ハウスドルフの局所コンパクト位相群上で定義された関数に作用する一般化フーリエ変換を扱う調和解析の一分野に対する理解が深まった。

Details

Sense（1）

WIENER [1] goes well beyond analysis of periodic functions on R or even functions in 𝔏₂(R); this important paper has yet to be interpreted and assimilated into the standard repertory of abstract harmonic analysis.

Google Translation / DeepL Translation

Details

abstract harmonic analysis

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