an:04132946
Zbl 0692.47015
Karpushkin, V. N.
Refined uniform estimates of oscillatory integrals and areas
RU
Usp. Mat. Nauk 43, No. 5(263), 197-198 (1988).
00184271
1988
j
47A55 26D10 58J40 42B99
oscillatory integral; canonical Maslov's operator
Let f: \(R^ 2\to R\), \(\phi\) : \(R^ 2\to R\) and
\[
I(\tau,f,\phi)=\int_{R^ 2}\phi \exp \{i\tau f\},\quad V(\epsilon,f,c,\phi,A)=\int_{R^ 2}\chi \phi,
\]
where \(\chi\) is the indicator of the set \(\{x\in A:\quad c-\epsilon \leq f(x)\leq c+\epsilon \}\) and A is an open set. In the paper some uniform two-term upper estimates for \(| I(\tau,f,\phi)|\) and \(| V(\epsilon,f,c,\phi,A)|\) are obtained.
Yu.M.Ry??ov