分段线性基小波变换在汉克尔变换评估中的应用
Application of the Wavelet Transform with a Piecewise Linear Basis to the Evaluation of the Hankel Transform
AI总结：
提出一种通过小波分解将被积函数表示为光滑函数乘以贝塞尔函数，从而将汉克尔变换简化为级数求和的方法，并利用示例展示了其应用。
摘要：
提出了一种计算汉克尔变换的方法，该方法通过将被积函数表示为光滑函数乘以贝塞尔函数，将其简化为求和。光滑函数被替换为其小波分解，使用一种基函数，使得其与贝塞尔函数的内积可以解析计算。结果表示为一个级数，其中系数强烈依赖于被变换函数的局部行为。通过一个示例展示了该方法的应用，并附有图示。
英文摘要：
A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a basis such that its scalar product with the Bessel function is calculated analytically. The result is represented as a series, with the coefficients strongly depending on the local behavior of the function being transformed. The application of the method is demonstrated by an example illustrated with plots.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
