Title   name
2018 KAIST Math. Colloquium
 
  Title
  Speaker   김준일    
  Date 2018-05-03
  Host
  Place KAIST
  File  의 1 번째 Real Media 동영상입니다.
 
Abstract : Given real valued polynomials $P$ on $mathbb{R}^n$ and various unbounded domains $D subset mathbb{R}^n$, we consider the oscillatory integrals

$$

I(P, D, lambda) = int_D e^{ilambda P(t)} dt.

$$

We establish a criterion on $(P, D)$ to determine the convergence of these integrals, and find the oscillation indices when they converge. These indices are described in terms of a generalized notion of Newton polyhedra associated with $(P, D)$. When $(P, D)$ for $D=mathbb{R}^n$ satisfies the criterion of the vector polynomial version $(t_1, cdots, t_n, P(t))$, we obtain the Strichartz estimates for the following general linear propagators:

$
e^{it P(D)}(f)(x) text{ where } D=left(frac{partial_{x_1}}{i}, cdots, frac{partial_{x_n}}{i} right).
$