Boundedness of the Segal-Bargmann Transform on Fractional Hermite-Sobolev Spaces

Cho, Hong Rae; Choi, Hyunil; Lee, Han-Wool

doi:10.1155/2017/9176914

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Fractional Radial Derivatives1

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Cited by 2 publications

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“…Moreover, we can see that is the infinitesimal generator of . That is, See [5] for more properties concerning the heat semigroup as well as the spectral property of the operator .…”

Section: Fractional Radial Derivativesmentioning

confidence: 95%

Fractional Fock–sobolev Spaces

Cho¹,

Park²

2018

Nagoya Math. J.

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Let $s\in \mathbb{R}$ and $0<p\leqslant \infty$. The fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,p}$ are introduced through the fractional radial derivatives $\mathscr{R}^{s/2}$. We describe explicitly the reproducing kernels for the fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,2}$ and then get the pointwise size estimate of the reproducing kernels. By using the estimate, we prove that the fractional Fock–Sobolev spaces $F_{\mathscr{R}}^{s,p}$ are identified with the weighted Fock spaces $F_{s}^{p}$ that do not involve derivatives. So, the study on the Fock–Sobolev spaces is reduced to that on the weighted Fock spaces.

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“…Moreover, we can see that is the infinitesimal generator of . That is, See [5] for more properties concerning the heat semigroup as well as the spectral property of the operator .…”

Section: Fractional Radial Derivativesmentioning

confidence: 95%