Asymptotic analysis in harmonic analysis by using Newton polyhedra

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K17565
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Fukuoka Institute of Technology (2016-2017); Kyushu Sangyo University (2015)
• Principal Investigator: NOSE Toshihiro 福岡工業大学, 工学部, 助教 (90637993)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: ニュートン多面体 / 振動積分 / 局所ゼータ関数 / トーリック・ブローアップ / 特異点解消 / 漸近解析 / 解析接続

Outline of Final Research Achievements

(1) We study toric blowing-ups related to Newton polyhedra. Using the blowing-ups, we locally represent the zero variety of smooth functions in simplified forms in two-dimensional cases. (2) We investigate the asymptotic behavior of oscillatory integrals with smooth phases in two dimensions. We have very interesting results such as log terms appearing in asymptotic limit of oscillatory integrals. (3) We show that local zeta functions can not be analytically continued as meromorphic functions across some point in some two dimensional smooth setting. In more general case, the region to which local zeta functions can be analytically continued as meromorphic functions are estimated by some geometrical information of Newton polyhedra.

Free Research Field

調和解析学