Image of Schwartz Space Under Spectral Projection

2007/12/26 by Joydip Jana, Jana, Joydip
Mathematics · #43A80 #43A85 #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Mathematical Analysis and Transform Methods #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0712.4117

openalex publication_date 2007/12/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X= G/K symmetric space of non compact type, where G is a rank-one connected semisimple Lie group with finite center. We shall look at the transform P_λf(x) = f ∗ φ_λ(x), where, λ∈ \mathbb C and φ_λ is the elementary spherical function. We shall try to characterizes the image of the Schwartz spaces S^p(X) where 0 < p ≤ 2 under the above transform.

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