Computational harmonic analysis - approximation of function

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540184
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: OKADA MASAMI 首都大学東京, 理工学研究科, 教授 (00152314)
• Co-Investigator(Kenkyū-buntansha): MORITOU SHINYA 奈良女子大学, 自然科学系, 教授 (30273832) ; UENO TOSHIHIDE 東京大学, 医学(系)研究科(研究院), 助教 (40381446) ; SAWANO YOSHIHIRO 首都大学東京, 大学院理工学研究科, 准教授 (40532635)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 実解析学 / サンプリング定理 / 多変数関数近似 / データ解析

Outline of Final Research Achievements

We investigated the general sampling theorem for scattered data in multi dimensional Euclidean　spaces, which means the reconstruction of unknown functions from their data observed on irregularly　scattered infinite points. In particular, we established the mathematical theory of the method　of using suitable positive definite functions. In fact we have succeeded in proving an optimal
approximate error estimate previously known for the regular sampling case and the applicability　of the method. One of the key points is a breakthrough on the multi dimensional polynomial　approximation.

Free Research Field

計算調和解析学、応用数理