The Mathematical Legacy of Leon Ehrenpreis

Authors professors of Politecnico di Milano

Leon Ehrenpreis has been one of the leading mathematicians in the twentieth century. His contributions to the theory of partial differential equations were part of the golden era of PDEs, and led him to what is maybe his most important contribution, the Fundamental Principle, which he announced in 1960, and fully demonstrated in 1970. His most recent work, on the other hand, focused on a novel and far reaching understanding of the Radon transform, and offered new insights in integral geometry. Leon Ehrenpreis died in 2010, and this volume collects writings in his honor by a cadre of distinguished mathematicians, many of which (Farkas, Kawai, Kuchment, Quinto) were his collaborators.

The only comparable titles in existence are the two volumes published in 1990 and in 2000, for (respectively) his 60th and his 70th birthday (the first one out of print, while the second one offering a perspective of the state of the art in integral geometry, partial differential equations, and Fourier analysis which is now ten years old)

Analyticity on Curves by M. Agranovsky, L. Zalcman.- On local injectivity for generalized Radon transforms by J. Boman.- Deconvolution for the Pompeiu problem on the Heisenberg group by Der-Chen Chang, W. Eby, E. Grinberg.- Theta Functions Wronskians and Weierstrass Points for Linear Spaces of Meromorphic Functions by H.M. Farkas.- The admissibility theorem for the spatial X-ray transform over the two element field by E.L. Grinberg.- Microlocal analysis of fixed singularities of WKB solutions of a Schroedinger equation by S. Kamimoto, T. Kawai, Y. Takei.- Geometric Properties of Boundary Orbit Accumulation Points by S.G. Krantz.-Microlocal Analysis of Elliptical Radon Transforms with Foci on a Line by V.P. Krishnan, H. Levinson, E. Todd Quinto.- Mathematics of Hybrid Imaging A Brief Review by P. Kuchment.- On Fermat type functional and partial differential equations dedicated to the memory of the late Professor Leon Ehrenpreis by Bao Qin Li.- An analogue of the Galois correspondence for foliations by B. Malgrange.- A Quantitative Version of Caratheodory's Theorem for Convex Sets by R. Meise, B.A. Taylor.- Geometric Path Integrals. A Language for Multiscale Biology and Systems Robustness by D. Napoletani, E. Petricoin, D.C. Struppa.- Bounded cohomology for solutions of systems of differential equations: applications to extension problems by I. Sabadini, D.C. Struppa.- On two lacunary series and modular curves by A. Sebbar.- PT symmetry and Weyl asymptotics by J. Sjostrand.- Complex Gradient Systems by G. Tomassini, S. Venturini.- Coleff-Herrera currents revisited by A. Vidras, A. Yger.- Right inverses for P(D) in spaces of real analytic functions by D. Vogt.- Averaging residue currents and the Stuckrad-Vogel algorithm by A. Yger.-