I'm interested in evaluation of integrals of the form $$\int e^{i S(x)}O(x) dx,$$
where $S(x)$ is a polynomial of degree higher than one and $O(x)$ is a polynomial or more generally, polynomialy bounded smooth function ($|O(x)|
General theory of divergent, highly oscillatory integrals
2
$\begingroup$
fourier-analysis
improper-integrals
distribution-theory
harmonic-analysis
oscillatory-integral
1 Answers
3
Yes. The theory of Lagrangian distributions also known as Fourier Integral Operators.
See Hormander's papers Fourier Integral Operators I and II.
Or volume IV of his book.
Or Duistermaat's book on Fourier Integral Operators. (this is more readable.)