标题： 理论的改进和Sinc卷积的收敛性 显示英文标题

标题： Refinement of the theory and convergence of the Sinc convolution

摘要： Sinc卷积是由Stenger提出的不定卷积的近似公式。 该公式是基于结合单指数变换的Sinc不定积分公式推导而来的。 尽管其在各个领域中的效率已被确认，但仍有几个理论问题尚未解决。 本研究的第一个贡献是通过改进Sinc卷积的基础理论来解决这些问题。 这一贡献包括对Stenger猜想的实质性解决。 本研究的第二个贡献是通过将单指数变换替换为双指数变换来提高收敛速度。 理论分析和数值实验证实，修改后的公式相比Stenger的原始公式具有更优的收敛性。 显示英文摘要

摘要： The Sinc convolution is an approximate formula for indefinite convolutions proposed by Stenger. The formula was derived based on the Sinc indefinite integration formula combined with the single-exponential transformation. Although its efficiency has been confirmed in various fields, several theoretical issues remain unresolved. The first contribution of this study is to resolve those issues by refining the underlying theory of the Sinc convolution. This contribution includes an essential resolution of Stenger's conjecture. The second contribution of this study is to improve the convergence rate by replacing the single-exponential transformation with the double-exponential transformation. Theoretical analysis and numerical experiments confirm that the modified formula achieves superior convergence compared to Stenger's original formula.