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<p>In this paper, we examine the convergence of sampling expansions in shift-invariant spaces with smooth generators for fundamentally large classes of functions. We establish the rate of approximation of a signal (not necessarily continuous) by the sampling series in terms of an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-average modulus of smoothness. We investigate the convergence and error analysis of sampling and projection operators based on Gaussian generators. Finally, we discuss the possibility of predicting a signal solely from past samples using sampling series based on Gaussian generators.</p>

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Approximation from shift-invariant spaces with smooth generators

  • 期刊论文

  • 发表日期：

    2025年4月8日

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  • A. Antony Selvan,
  • Ayush Bhandari,
  • R. Radha

摘要

In this paper, we examine the convergence of sampling expansions in shift-invariant spaces with smooth generators for fundamentally large classes of functions. We establish the rate of approximation of a signal (not necessarily continuous) by the sampling series in terms of an \(L^p\) L p -average modulus of smoothness. We investigate the convergence and error analysis of sampling and projection operators based on Gaussian generators. Finally, we discuss the possibility of predicting a signal solely from past samples using sampling series based on Gaussian generators.