Duality results for a general trigonometric approximation problem

2017/11/21 by Lutz Klotz, Klotz, Lutz, Conrad Mädler +1
Mathematics · #41A65 #42A10 #43A15 #60G25 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1711.07708

openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let α∈(1,∞) and μ be a regular finite Borel measure on a locally compact abelian group. The paper deals with a general trigonometric approximation problem in L^α(μ), which arises in prediction theory of harmonizable symmetric α-stable processes. To solve it, a duality method is applied, which is due to Nakazi and was generalized by Miamee and Pourahmadi and in the sequel successfully applied by several authors. The novelty of the present paper is that we do not make any additional assumption on μ. Moreover, for α=2, multivariate extensions are obtained.

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