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Algebraically integrable bodies and related properties of the Radon transform
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Mark Agranovsky
Abstract
Generalizing Lemma 28 from Newton’s “Principia” [25], Arnold [10] asked for a complete characterization of algebraically integrable domains. In this chapter we describe the current state of Arnold’s problems. We also consider closely related problems involving the Radon transform of indicator functions.
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Abstract
Generalizing Lemma 28 from Newton’s “Principia” [25], Arnold [10] asked for a complete characterization of algebraically integrable domains. In this chapter we describe the current state of Arnold’s problems. We also consider closely related problems involving the Radon transform of indicator functions.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
Kapitel in diesem Buch
- Frontmatter I
- Contents V
- Algebraically integrable bodies and related properties of the Radon transform 1
- The covariogram problem 37
- The logarithmic Minkowski conjecture and the Lp-Minkowski problem 83
- Bellman functions and continuous time 119
- Volume product 163
- Inequalities for sections and projections of convex bodies 223
- Borderline estimates for weighted singular operators and concavity 257
- Extremal sections and projections of certain convex bodies: a survey 343
- When does e−/τ/ maximize Fourier extension for a conic section? 391
- Affine surface area 427
- Analysis and geometry near the unit ball: proofs, counterexamples, and open questions 445
- Index 469
