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Jiming Shen,
Danyang Tian, and
Yixin Yang
The complete Nevanlinna-Pick property for sub-Bergman Hilbert spaces
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| Published: |
October 13, 2025. |
| Keywords: |
Sub-Bergman Hilbert space; complete Nevanlinna-Pick property; polydisk; inner function. |
| Subject [2010]: |
Primary 46E22; Secondary 30H10. |
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Abstract
In this paper, we show that for non-constant ϕ in H1∞(Dn), the sub-Bergman Hilbert space H(Knϕ) over the n-disk with n greater than 1 does not have the complete Nevanlinna-Pick property. Furthermore, we prove by different methods that if ϕ is an inner function on D, the corresponding sub-Bergman Hilbert space on D has the complete Nevanlinna-Pick property if and only if ϕ is a Mobius map ([6]).
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| Acknowledgements
This research is supported by National Science Foundation of China (No.12471117) and the Fundamental Research Funds for the Central Universities (DUT24LAB128).
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| Author information
Jiming Shen
School of Mathematical Sciences
Dalian university of Technology
Dalian 116024, Peoples Republic of China
Shenjiming@mail.dlut.edu.cn
Danyang Tian
School of Mathematical Sciences
Dalian university of Technology
Dalian 116024, Peoples Republic of China
Tiandanyang@mail.dlut.edu.cn
Yixin Yang
School of Mathematical Sciences
Dalian university of Technology
Dalian 116024, Peoples Republic of China
yangyixin@dlut.edu.cn
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