## Tuesday Seminar of Analysis

Date, time & place Tuesday 16:00 - 17:30 126Room #126 (Graduate School of Math. Sci. Bldg.) ISHIGE Kazuhiro, SAKAI Hidetaka, ITO Kenichi

### 2022/12/20

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
KATAOKA Kiyoomi (The University of Tokyo)
A commentary on J. Boman's recent two related results about the support of a distribution and its analyticity, and a special relationship between Radon transformations and ellipsoidal regions (Japanese)
[ Abstract ]
Jan Boman's (Stockholm Univ.) recent two papers:
[1], Regularity of a distribution and of the boundary of its support, The Journal of Geometric Analysis vol.32, Article number: 300 (2022).
[2], A hypersurface containing the support of a Radon transform must be an ellipsoid. II: The general case; J. Inverse Ill-Posed Probl. 2021; 29(3): 351–367.
In [1] he proved "Let $f(x_1,…,x_n,y)$ be a non-zero distribution with support in a $C^1$ surface $N=\{y=F(x)\}$. If $f(x,y)$ is depending real analytically on x-variables, then $F(x)$ is analytic". As an application, he reinforced the main result of [2]. These results are obtained essentially by means of matrix algebra and a number theoretic method.
[ Reference URL ]
https://forms.gle/BpciRTzKh9FPUV8D7