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F. 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。 尽管其在多个领域中的效率已被确认，但其理论中仍存在一些未解的问题。 本研究的第一个贡献是通过改进Sinc卷积的理论来解决这些问题。 这一贡献包括对Stenger猜想的部分解决。 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。 在理论和数值方面，本研究还表明，新公式的收敛速度优于Stenger公式。 显示英文摘要

摘要： The Sinc convolution is an approximate formula for indefinite convolutions proposed by F. 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 variety of areas, there remain some open problems in its theory. The first contribution of this study is to resolve those problems by refinement of the theory of the Sinc convolution. This contribution includes a partial resolution of Stenger's conjecture. The second contribution of this study is to improve the convergence rate by replacement of the single-exponential transformation with the double-exponential transformation. In both theoretical and numerical ways, this study also shows that the convergence rate of the new formula is improved compared to Stenger's formula.