Fourier Analysis In Convex Geometry pdf book This conference is on the interface between convex geometry and harmonic analysis. Alexander Koldobsky will deliver ten lectures on a number of topics of Harmonic Analysis and Uniqueness Questions in Convex Geometry Alexander Koldobsky Mathematics-University of Missouri, Columbia the interface between convex geometry and harmonic analysis free. In mathematics, convex geometry is the branch of geometry studying convex sets,. V. Yaskin, The Interface between Convex Geometry and Harmonic Analysis, Applications of Fourier analysis to convex geometry A typical result we prove is that if r ? 2 and X ? r Y ? I p where p ? 2 then X ? I q as long as p ? q ? m + p where m dim Y. We consider a more general Alexander Koldobsky-Google Scholar Citations A.Koldobsky, V.Yaskin, The interface between convex geometry and harmonic analysis, CBMS Regional Conference Series, American Mathematical Society, The Interplay between Convex Geometry and Harmonic Analysis the interface between convex geometry and harmonic analysis free pdf and manual. The book is written in the form of lectures accessible to graduate students. This approach allows the reader to clearly see the main ideas behind the method, Convex geometry-Wikipedia, the free encyclopedia This workshop, sponsored by AIM and the NSF, concerns the interface between convex geometry and harmonic analysis. Particular attention will be given to A Course on Convex Geometry The Interface Between Convex Geometry and Harmonic Analysis. 26 Dec 2013. in convex geometry, asks whether there exists an absolute constant C. Geometry of Banach spaces and harmonic analysis, Proceedings KY A. Koldobsky and V. Yaskin, The Interface between Convex Geometry and. Upcoming Scientific Events-MSRI 14 Mar 2014. For Organizers • For Applicants • Reply to a Workshop Invitation • Organizer Interface • BIRS Geometric Tomography and Harmonic Analysis 14w5085 to coordinate the main applications of Harmonic Analysis to Convex Geometry and the duality between sections and projections of convex bodies. A hyperplane inequality for measures of unconditional convex bodies Contents.

We apply Fourier transforms to homogeneous extensions of functions on S n−1 . This results in complex integral operators. The real and imaginary parts of these operators provide a pairing of stereological data that leads to new results concerning the determination of convex bodies as well as new settings for known results. Applying the Funk-Hecke theorem to these operators yields stability versions of the results.

Abstract. Suppose that we have the unit Euclidean ball in R n and construct new bodies using three operations -linear transformations, closure in the radial metric, and multiplicative summation defined byWe prove that in dimension 3 this procedure gives all origin-symmetric convex bodies, while this is no longer true in dimensions 4 and higher. We introduce the concept of embedding of a normed space in L 0 that naturally extends the corresponding properties of L p -spaces with p = 0, and show that the procedure described above gives exactly the unit balls of subspaces of L 0 in every dimension. We provide Fourier analytic and geometric characterizations of spaces embedding in L 0 , and prove several facts confirming the place of L 0 in the scale of L p -spaces.

For −1 < p < 1 we introduce the concept of a polar pcentroid body Γ * p K of a star body K. We consider the question of whether Γ * p K ⊂ Γ * p L implies vol(L) ≤ vol(K). Our results extend the studies by Lutwak in the case p = 1 and Grinberg, Zhang in the case p > 1.

The Busemann-Petty problem asks whether originsymmetric convex bodies in R n with smaller central hyperplane sections necessarily have smaller n-dimensional volume. It is known that the answer is affirmative if n ≤ 4 and negative if n ≥ 5. In this article we modify the assumptions of the original Busemann-Petty problem to guarantee the affirmative answer in all dimensions.