Reproducing kernels and integral transforms

再现内核和积分变换

• 批准号: 60540086
• 负责人: SAITOH Saburou
• 金额: $ 0.38万
• 依托单位: Gunma University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1985
• 资助国家: 日本
• 起止时间: 1985 至 1986
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60540086/
• 关键词: Reproducing kernel; Integral transform; Convolution; Laplace transform; Fourier transform; Paley-Wiener's theorem; ピックネバンリンナの問題

We developed a general theory of integral transforms and showed miscellaneous applications to : Cauchy integral formula, Poisson integral formula, the solutions of differential equations, interpolation problems for analytic and harmonic functions of class <L_2> , and Fourier-Laplace transforms on tube domains.Moreover, as applications of the theory of reproducing kernels, the idea of nonharmonic integral transforms, interpolation problems of Pick-Nevanlinna type and miscellaneous norm inequalities are derived.

We developed a general theory of integral transforms and showed miscellaneous applications to : Cauchy integral formula, Poisson integral formula, the solutions of differential equations, interpolation problems for analytic and harmonic functions of class <L_2> , and Fourier-Laplace transforms on tube domains.Moreover, as applications of the theory of reproducing kernels, the idea of​​ nonharmonic integral transforms, interpolation problems of提出了挑选的Nevanlinna类型和其他规范不平等。

项目成果

Saburou Saitoh: Linear Algehra and Applications. (1987)

Saburou Saitoh：线性代数及其应用。

Saburou Saitoh: "Generalizations of Paley-Wiener's theorem for entire functions of exponential type" Proc. Amer. Math. Soc.99. (1987)

Saburou Saitoh：“指数型整个函数的 Paley-Wiener 定理的推广”Proc。

Saburou Saitoh: Math.Vesnik. 37. 121-133 (1985)

齐藤三郎：Math.Vesnik。

Saburou Saitoh: Kodai Math.J.9. 50-57 (1986)

齐藤三郎：Kodai Math.J.9。

Saburou Saitoh: "The Laplace transform of <L^p> functions with weights" Applicable Analysis. 22. 103-109 (1986)

Saburou Saitoh：“带权重的 <L^p> 函数的拉普拉斯变换”适用分析。