标题： 某些复数Nevai算子的逼近：理论与应用 显示英文标题

标题： Approximation by Certain Complex Nevai Operators : Theory and Applications

摘要： 复值函数的逼近在理论上具有重要意义，因为它将经典的逼近理论推广到复数域，为与幅度和相位相关的现象提供了严格的框架。 在本文中，我们研究了Nevai算子，这是一个由著名数学家Paul G. Nevai提出的概念。 我们提出了一类复Nevai插值算子，用于逼近解析的以及非解析的复值函数，并结合了图像处理中的实际应用。 在这方面，第一个算子是使用第一类切比雪夫多项式构造的，即用于逼近复值连续函数的复广义Nevai算子。 我们利用连续性模的概念建立了所提出算子的逼近结果。 为了逼近不一定是连续但可积的函数，我们定义了复Kantorovich型Nevai算子，并建立了它们的有界性和收敛性。 此外，为了逼近保持高阶导数的函数，我们引入了复Hermite型Nevai算子，并利用高阶连续性模研究了它们的逼近能力。 为了验证理论结果，我们提供了所提出复Nevai算子族逼近能力的数值示例。 显示英文摘要

摘要： The approximation of complex-valued functions is of fundamental importance as it generalizes classical approximation theory to the complex domain, providing a rigorous framework for amplitude and phase-dependent phenomena. In this paper, we study the Nevai operator, a concept formulated by the distinguished mathematician Paul G. Nevai. We propose a family of complex Nevai interpolation operators to approximate analytic as well as non-analytic complex-valued functions along with real-life application in image processing. In this direction, the first operator is constructed using Chebyshev polynomials of the first kind, namely complex generalized Nevai operators for approximating complex-valued continuous functions. We establish the approximation results for the proposed operators utilizing the notion of a modulus of continuity. To approximate not necessary continuous but integrable function, we define complex Kantorovich type Nevai operators and establish their boundedness and convergence. Furthermore, in order to approximate functions preserving higher derivatives, we introduce complex Hermite type Nevai operators and study their approximation capabilities using higher order of modulus of continuity. To validate the theoretical results, we provide numerical illustrations of approximation abilities of proposed family of complex Nevai operators.