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Comments and Open Problems

In: Integral Geometry and Convolution Equations

Author

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  • V. V. Volchkov

    (Donetsk National University, Department of Mathematics)

Abstract

The first example of nonzero function with vanishing integrals over balls with fixed radii was considered by L. Chakalov [C3] (see also [J1]–[J3] for the case of spherical averages). Some properties of the class V r s (B r ), related to expansion in spherical harmonics have been studied by the author [V10], [V18]. In particular, the results of Section 1.1 have been obtained in the papers [V18], [V24]. The examples of functions in the class V r (B r ) constructed in Section 1.1 can be use in studying a nontrivial estimates for the density of packings of balls with fixed radius (see Chapter 5.8).

Suggested Citation

  • V. V. Volchkov, 2003. "Comments and Open Problems," Springer Books, in: Integral Geometry and Convolution Equations, chapter 0, pages 137-142, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0023-9_13
    DOI: 10.1007/978-94-010-0023-9_13
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