Geodesic
On the uniqueness of continuation for polynomials of harmonic quaternion fields
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 102-106

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The paper provides a counterexample to the hypothesis on the uniqueness of continuation for polynomials of harmonic quaternion fields in a compact domain with a nonanalytic metric. The constructed polynomial vanishes identically in a neighborhood of the boundary. A connection of this construction with the problem on resonances of the Schroedinger operator on a line is noted. 
@article{ZNSL_2020_493_a7,
     author = {A. F. Vakulenko},
     title = {On the uniqueness of continuation for polynomials of harmonic quaternion fields},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {102--106},
     publisher = {mathdoc},
     volume = {493},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a7/}
}
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A. F. Vakulenko. On the uniqueness of continuation for polynomials of harmonic quaternion fields. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 50, Tome 493 (2020), pp. 102-106. http://geodesic.mathdoc.fr/item/ZNSL_2020_493_a7/