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Survey of recent developments on the Pompeiu problem and the Schiffer problem. This problem has surprising interactions with inverse scattering, image processing and other applied problems.

Notes of a graduate course given in Venice, Italy, during June 1996 organized by CIME, directed to graduate students to show the interplay of different kinds of Radon transforms and medical and material science problems

Lecture presented at Taniguchi Symposium, Katata, June 1995. Deals with new kind of differential equations for multivalued functions. The monodromy operator is allowed to enter into the equation. Related to resurgence and ...

We provide new tools to compute multidimensional residues for rational functions, even over fields of positive characteristic. As a corollary one obtains solutions of the Betout equation for polynomials over a ring with a ...

We show that solid tori in Rn satisfy the Pompeiu property: This problem remains open for dimensions n ﺠ4.

We study the relation between convolution operators and the totally geodesic Radon transform on hyperbolic spaces. as an application we show that the linearized inverse conductivity problem in the disk can be interpreted ...

This is a reprint of a 1976 paper that appears in an inaccessible Brazilian journal and has become very looked after. It deals with the problem of determining a convex plane domain from the existence of infinitely many ...

Lecture delivered at Research Institute for Mathematical Sciences, Kyoto University, Symposium on Algebraic Analysis, July 1995. Explains the relationship between new kinds of D-modules and ideals of exponential polynomials.

We develop an algorithm to reconstruct the wavelet coefficients of an image from the Radon transform data. The proposed method uses the properties of wavelets to localize the Radon transform and can be used to reconstruct ...

Some explicit formulas are provided in order to solve division problems in commutative algebra or questions related to intersection theory; it is shown here how the ides of analytic continuation of distributions leads to ...