Approximation properties of multivariate exponential sampling series
Sadettin Kursun, Metin Turgay, Osman Alagöz, Tuncer Acar
Abstract
In this paper, we generalize the family of exponential sampling series for functions of $n$ variables and study their pointwise and uniform convergence as well as the rate of convergence for the functions belonging to space of $\log$-uniformly continuous functions. Furthermore, we state and prove the generalized Mellin-Taylor's expansion of multivariate functions. Using this expansion we establish pointwise asymptotic behaviour of the series by means of Voronovskaja type theorem.
Topics & Concepts
MathematicsPointwisePointwise convergenceSeries (stratigraphy)Taylor seriesExponential functionConvergence (economics)Multivariate statisticsRate of convergenceApplied mathematicsExponential typeUniform convergenceSampling (signal processing)Asymptotic expansionMathematical analysisStatisticsKey (lock)Bandwidth (computing)PaleontologyComputer scienceApproxEconomic growthEconomicsOperating systemComputer networkBiologyComputer visionFilter (signal processing)EcologyApproximation Theory and Sequence SpacesMathematical Approximation and IntegrationAdvanced Harmonic Analysis Research