论文标题
对调制空间的元容器
The metaplectic action on modulation spaces
论文作者
论文摘要
我们研究了跨度运算符的映射属性$ \ wideHat {s} \ in \ mathrm {mp}（2d，\ mathbb {r}）$在类型的调制空间上我们的主要结果是对$（\ wideHat {s}，\ Mathrm {m}^{p，q，q}（\ Mathbb {r}^d））$的完整表征。 \ Mathrm {M}^{P，Q}（\ Mathbb {r}^d）$是（i）定义明确，（ii）边界。事实证明，这两个属性是等效的，他们需要$ \ wideHat {s} $是Banach Space自动形态。对于多项式限制的重量函数，我们提供了一个简单的足够标准来确定$ {\ wideHat {s} {s} {s}：\ mathrm {M}^{ \ Mathrm {m}^{p，q}（\ Mathbb {r}^d）} $将$ Transfers转移到$ \ wideHat {s} {s}：\ Mathrm {m}^{ \ mathrm {m}^{p，q} _m（\ mathbb {r}^d）$。
We study the mapping properties of metaplectic operators $\widehat{S}\in \mathrm{Mp}(2d,\mathbb{R})$ on modulation spaces of the type $\mathrm{M}^{p,q}_m(\mathbb{R}^d)$. Our main result is a full characterisation of the pairs $(\widehat{S},\mathrm{M}^{p,q}(\mathbb{R}^d))$ for which the operator $\widehat{S}:\mathrm{M}^{p,q}(\mathbb{R}^d) \to \mathrm{M}^{p,q}(\mathbb{R}^d)$ is (i) well-defined, (ii) bounded. It turns out that these two properties are equivalent, and they entail that $\widehat{S}$ is a Banach space automorphism. For polynomially bounded weight functions, we provide a simple sufficient criterion to determine whether the well-definedness (boundedness) of ${\widehat{S}:\mathrm{M}^{p,q}{}(\mathbb{R}^d)\to \mathrm{M}^{p,q}(\mathbb{R}^d)}$ transfers to $\widehat{S}:\mathrm{M}^{p,q}_m(\mathbb{R}^d)\to \mathrm{M}^{p,q}_m(\mathbb{R}^d)$.
