On asymptotic expansions of oscillatory integrals with phase functions expressed by a product of positive real power function and real analytic function in one variable

2020/10/21 by Nagano, Toshio
#33B20 #41A60 #42B20 #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2010.11141

Abstract

In this paper, by using asymptotic expansions of oscillatory integrals with positive real power phase functions in one variable, we obtain asymptotic expansions of oscillatory integrals with phase functions expressed by a product of positive real power function and real analytic function in one variable. Moreover we show an example which we can compute all coefficients of terms in asymptotic expansions concretely.

Related

• Oscillatory integrals with phase functions of positive real powers and asymptotic expansions
• Generalized Fresnel integrals as oscillatory integrals with positive real power phase functions and applications to asymptotic expansions
• On oscillatory integrals associated to phase functions with degenerate singular points
• Asymptotic expansions of oscillatory integrals with complex phase
• Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena