Characterizations of Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $

Xi Fu; Xiaoqiang Xie; Xi Fu; Xiaoqiang Xie

doi:10.3934/math.2022852

AIMS Mathematics

2022, Volume 7, Issue 8: 15550-15562. doi: 10.3934/math.2022852

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Research article

Characterizations of Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $

Xi Fu ^,,
Xiaoqiang Xie

Department of Mathematics, College of Arts and Sciences, Shanghai Polytechnic University, Shanghai 201209, China

Received: 27 March 2022 Revised: 16 June 2022 Accepted: 20 June 2022 Published: 23 June 2022
MSC : 31B05, 31B10, 30H20

In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on $ \mathbb{R}^n $. As applications, we characterize Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $ in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.
- eigenfunction,
- Fock space,
- Lipschitz condition,
- double integral condition
Citation: Xi Fu, Xiaoqiang Xie. Characterizations of Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $[J]. AIMS Mathematics, 2022, 7(8): 15550-15562. doi: 10.3934/math.2022852

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Abstract

In this paper, we prove a norm equivalence for an exponential type weighted integral of an eigenfunction and its derivative on $ \mathbb{R}^n $. As applications, we characterize Fock-type spaces of eigenfunctions on $ \mathbb{R}^n $ in terms of Lipschitz type conditions and double integral conditions. These obtained results are extensions of the corresponding ones in classcial Fock space.

References

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