Comparison of generalized Fourier and wavelet expansions in function spaces

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400138
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nara Women's University
• Principal Investigator: MORITOH Shinya 奈良女子大学, 自然科学系, 教授 (30273832)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: フーリエ解析 / ワイル・ストーン・ティッチマーシュ・小平の定理 / 函数空間 / 重み付き不等式 / ウェーブレット解析

Outline of Final Research Achievements

The main idea of this research is the intimate relation between the smoothness of a function and the decay of its Fourier transform. We use the Weyl-Stone-Titchmarsh-Kodaira theorem on general expansions. The main subjects are as follows; (1) to give a generalization of the condition on associated density functions, (2) to consider the distribution of eigenvalues for the operators under consideration, and (3) to reconsider the problem in light of wavelet theory. One of the techniques is to give a weighted inequality in Besov spaces. This research comes from classical analysis, and an ability to use a classical method is essential. Such a collection of knowledge will become important in our future research.

Free Research Field

フーリエ解析