1998 Fiscal Year Final Research Report Summary
Algebraic Analysis of Exponential Asymptotics
| Project/Area Number |
09640234
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Kinki University |
|---|
Principal Investigator |
AOKI Takashi Kinki University, Department of Mathematics, Professor, 理工学部, 教授 (80159285)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OWA Shigeyoshi Kinki University, Dept.of Mathematics, Professor, 理工学部, 教授 (50088506)
IZUMI Shuzo Kinki University, Dept.of Mathematics, Professor, 理工学部, 教授 (80025410)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | Stokes geometry / Painleve equations / 3d order O.D.E. / transcendence / exponential asymptotics / p-valent functions / Duffing equation / multiple-scale analysis / formal functions |
|---|
| Research Abstract |
・2-paramnetered exponential asymptotic solution to the Dufling equation is constructed by using the multiple-scale analysis. It is proved that the formal solution converges and coincides with the ・Fourier series expansion of the solution written in terms of Jacobi's elliptic function obtained by quadrature.
・The Stokes geometry of the second and the third Painleve equations are determined.
・An Ansatz concerning determination of Stokes gepmetry of third order ordinary differential equations with a large parameter is proposed. In the case where the solutions have integral representations, the Stokes geometries obtained by the Ansatz are consistent with the Stokes phenomen detected by using the method of the steepest descent paths.
・A measure which measures transcendence of a finite subset of a local ring. It is proved that the measure is finite for some family of special functions in the formal power series ring.
・An extension of Gabrielov's theorem to the formal functions is obtained.
・A differential operator acting on the space of p-valent meromorphic functions is introduced and some differential inequalities for the family of p-valent meromorphic functions are obtained by using them.
・For analytic functions on the unit disk that vanish on the origin and the derivative there is identical, distortion inequalities that contains Ruscheweyh derivatives are obtained.
|
