English Dictionary

coorbit theory

名詞

不可算名詞

(mathematics) A theory for atomic decomposition of a range of Banach spaces of distributions, including among others the wavelet transform and the short-time Fourier transform.

日本語の意味

（数学）分布のバナッハ空間の範囲において、関数や分布を原子（基本的要素）に分解する理論。具体的には、ウェーブレット変換や短時間フーリエ変換などの手法が含まれる。

Recent research in harmonic analysis uses coorbit theory to construct atomic decompositions for signal spaces arising from the wavelet and short-time Fourier transforms.

最近の調和解析の研究では、ウェーブレット変換や短時間フーリエ変換などを含む、分布のさまざまなバナッハ空間の原子的分解に関する理論を用いて、信号空間の原子的分解を構築しています。

意味（1）

(mathematics) A theory for atomic decomposition of a range of Banach spaces of distributions, including among others the wavelet transform and the short-time Fourier transform.

For Besov-Triebel-Lizorkin spaces, one uses a dyadic decomposition, while a uniform decomposition yields modulation spaces. Only recently, the second author has established a fruitful connection between modern variants of wavelet theory with respect to general dilation groups (which can be treated in the context of coorbit theory) and a particular family of decomposition spaces.