Random Average Sampling in a Reproducing Kernel Subspace of Mixed Lebesgue Space L<SUP>p,q</SUP>(R<SUP>n+1</SUP>)

作     者：Patel, Dhiraj Sivananthan, S. 

作者机构：Indian Inst Technol Delhi Dept Math New Delhi 110016 India 

出 版 物：《RESULTS IN MATHEMATICS》 (数学成果)

年 卷 期：2024年第79卷第1期

页      面：9-9页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：We are grateful to the anonymous referee for meticulously reading the manuscript and giving us helpful suggestions. The authors thank IIT Delhi HPC facility for computational resources. The first author acknowledges Council of Scientific amp Industrial R [CRG/2019/002412] Council of Scientific amp Industrial Research Department of Science and Technology, Government of India 

主　　题：Reproducing kernel space mixed Lebesgue space random sampling reconstruction algorithm Idempotent operator Average sampling inequality 

摘      要：In this paper, we study average sampling inequality in a probabilistic framework for a reproducing kernel subspace V of mixed Lebesgue space. More precisely, we show with high probability that a function concentrated on a compact cube C can be stably recovered from their O(mu (C) log mu (C)) many average values at uniformly distributed random points over C, where mu is a Lebesgue measure. Further, we propose an exponential convergence reconstruction scheme to reconstruct the concentrated function from their random average measurements and illustrate with an example.