Abstract
We classify self-adjoint first-order differential operators on weighted Bergman spaces on the unit disc and answer questions related to uncertainty principles for such operators. Our main tools are the discrete series representations of \(\textrm{SU}(1,1)\). This approach has the promise to generalize to other bounded symmetric domains.
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Communicated by Daniel Alpay.
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Christensen, J.G., Deng, C.B. Uncertainty Principles and Differential Operators on the Weighted Bergman Space. Complex Anal. Oper. Theory 17, 47 (2023). https://doi.org/10.1007/s11785-023-01352-w
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DOI: https://doi.org/10.1007/s11785-023-01352-w