Functions with Vanishing Integrals over Ellipsoids

V. V. Volchkov
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V. V. Volchkov: Donetsk National University, Department of Mathematics

Chapter Chapter 4 in Integral Geometry and Convolution Equations, 2003, pp 271-302 from Springer

Abstract: Abstract Throughout in this chapter, n ≥ 2, a 1,...,a n are positive numbers, a = (a 1,..., a n ), and 4.1 $$ a_1 \leqslant a_2 \leqslant \ldots \leqslant a_n . $$ We denote $$ E_a = \left\{ {x \in \mathbb{R}^n :\sum\nolimits_{m = 1}^n {{{x_m^2 } \mathord{\left/ {\vphantom {{x_m^2 } {a_m^2 }}} \right. \kern-\nulldelimiterspace} {a_m^2 }}} \leqslant 1} \right\} $$ . In this section we shall study the functions with zero integrals over various collections of ellipsoids in ℝ n having a common center.

Keywords: Auxiliary Result; Exponential Type; Algebraic Polynomial; Nonzero Function; Common Center (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-010-0023-9_22

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DOI: 10.1007/978-94-010-0023-9_22

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