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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {2020},
     volume = {493},
     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/

[1] M. I. Belishev, N. D. Filonov, S. T. Krymskiy, A. F. Vakulenko, On uniqueness of continuation for polynomials of solutions to second-order elliptic PDE, Applicable Analysis, 2020

[2] M. I. Belishev, A. F. Vakulenko, “On algebraic and uniqueness properties of 3d harmonic quaternion fields”, CUBO A Mathematical J., 21:1 (2019), 1–19 | DOI | MR | Zbl

[3] E. Korotyaev, “Inverse Resonance Scattering on the Half Line”, Asymptot. Anal., 37 (1985), 215–226 | MR

[4] G. Schwarz, Hödge decomposition – a method for solving boundary value problems, Lect. Notes Math., 1607, Springer-Verlag, Berlin, 1995 | DOI | MR | Zbl