Abstract
An oscillatory integral of the form naturally defines a distribution provided that φ is a phase function and a is a symbol in Hormander's symbol class. In this paper extending this result to the case of Gevrey class we show that the above oscillatory integral defines a Gevrey ultradistribution provided that φ is a Gevrey phase function and a is a symbol in Gevrey symbol class of infinite order. We also prove the singular support theorem and the singular spectrum theorem which are important in application
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