@article{polynomial-ucp,
	author = {Joonas Ilmavirta and Keijo M{\"o}nkk{\"o}nen},
	title = {{Partial data problems in scalar and vector field tomography}},
	year = 2022,
	month = mar,
	journal = {Journal of Fourier Analysis and Applications},
	volume = 28,
	number = 34,
	arxiv = {2103.14385},
	url={http://users.jyu.fi/~jojapeil/pub/polynomial-ucp.pdf},
	abstract = {We prove that if~$P(D)$ is some constant coefficient partial differential operator and~$f$ is a scalar field such that~$P(D)f$ vanishes in a given open set, then the integrals of~$f$ over all lines intersecting that open set determine the scalar field uniquely everywhere. This is done by proving a unique continuation property of fractional Laplacians which implies uniqueness for the partial data problem. We also apply our results to partial data problems of vector fields.},
	doi = {10.1007/s00041-022-09907-9}
}