Abstract
We discuss Hesse’s conjecture for homogeneous polynomials and Korenblum’s conjecture on algebras of harmonic functions from the standpoint of nonlinear first-order PDE. Also, we extend a recent theorem of McKinley and Shekhtman for homogeneous polynomial partial differential operators to a wider class of linear PDE with entire coefficients.
Dedicated to the memory of S. Shimorin, an extraordinary mathematician and a kind and gentle man
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Acknowledgement
The author’s research was supported by the Simons Foundation Grant 513381.
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Khavinson, D. (2019). Remarks on the Interplay Between Algebra and PDE. In: Aleman, A., Hedenmalm, H., Khavinson, D., Putinar, M. (eds) Analysis of Operators on Function Spaces. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-14640-5_8
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DOI: https://doi.org/10.1007/978-3-030-14640-5_8
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