4 citations · 10 across the 5 of their papers we have counts for
5 papers
Oscillatory integrals with phase functions of positive real powers and asymptotic expansions
Toshio Nagano, Naoya Miyazaki
As to methods for expanding an oscillatory integral into an asymptotic series with respect to the parameter, the method of stationary phase for the non-degenerate phases and the me…
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
Toshio Nagano
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 inte…
On oscillatory integrals associated to phase functions with degenerate singular points
Toshio Nagano, Naoya Miyazaki
In this note, by using the result in one variable, we obtain asymptotic expansions of oscillatory integrals for certain multivariable phase functions with {\bf degenerate} singular…
Generalized Fresnel integrals as oscillatory integrals with positive real power phase functions and applications to asymptotic expansions
Toshio Nagano, Naoya Miyazaki
In this paper, we first generalize the Fresnel integrals by changing of a path for integration in the proof of the Fresnel integrals by Cauchy's integral theorem. Next, according t…
On Singular Points and Oscillatory Integrals
Toshio Nagano, Naoya Miyazaki
In this note, we generalize the Fresnel integrals using oscillatory integral, and then we obtain an extention of the stationary phase method.