Functions with Zero Averages Over Balls on Subsets of the Space ℝ n

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

Chapter Chapter 1 in Integral Geometry and Convolution Equations, 2003, pp 57-99 from Springer

Abstract: Abstract Let r > 0 be a fixed number and let $$ \mathcal{U} $$ be a domain in ℝ n containing a closed ball of radius r. Denote by V r $$ \mathcal{U} $$ the set of functions f ∈ L loc $$ \mathcal{U} $$ with zero averages over all closed balls of radius r lying in $$ \mathcal{U} $$ . For s ∈ ℕ+ or s = ∞ we set $$ V_r^s \left( \mathcal{U} \right) = \left( {V_r \cap C^s } \right)\left( \mathcal{U} \right) $$ .

Keywords: Asymptotic Formula; Uniqueness Theorem; Class Versus; Helmholtz Equation; Radial Function (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1007/978-94-010-0023-9_10

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