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Israel Journal of Mathematics

, Volume 161, Issue 1, pp 187–207 | Cite as

Approximation by K-finite functions in L p spaces

  • E. K. NarayananEmail author
  • R. Rawat
  • S. K. Ray
Article

Abstract

Let Γ ⊂ ℝn, n ≥ 2, be the boundary of a bounded domain. We prove that the translates by elements of Γ of functions which transform according to a fixed irreducible representation of the orthogonal group form a dense class in L p (ℝn) for \(p \geqslant \tfrac{{2n}}{{n + 1}}\). A similar problem for noncompact symmetric spaces of rank one is also considered. We also study the connection of the above problem with the injectivity sets for weighted spherical mean operators.

Keywords

Irreducible Representation Symmetric Space Radial Function Matrix Entry Real Analytic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© The Hebrew University of Jerusalem 2007

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Mathematics and StatisticsIndian Institute of Technology KanpurKanpurIndia

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