Translation invariance of Fock spaces
Kehe Zhu
TL;DR
This paper proves that the only Hilbert space of entire functions invariant under certain weighted translations is unique, highlighting a fundamental property of Fock spaces.
Contribution
It establishes the uniqueness of the Fock space as the only translation-invariant Hilbert space of entire functions.
Findings
Uniqueness of the translation-invariant Fock space
Characterization of invariant Hilbert spaces of entire functions
Foundational result in functional analysis and quantum mechanics
Abstract
We show that there is only one Hilbert space of entire functions that is invariant under the action of naturally defined weighted translations.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Operator Algebra Research · Advanced Topics in Algebra