We consider weighted Radon transforms RW along hyperplanes in R 3 with strictly positive weights W. We construct an example of such a transform with non-trivial kernel KerRW in the space of infinitely smooth compactly supported functions and with continuous weight. Moreover, in this example the weight W is rotation invariant. In particular, by this result we continue studies of Quinto (1983), Markoe, Quinto (1985), Boman (1993) and Goncharov, Novikov (2017). We also extend our example to the case of weighted Radon transforms along two-dimensional planes in R d , d $\ge$ 3. 查看全文>>