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- W2950308124 abstract "We call a function if it has a globally subanalytic domain and can be expressed as a sum of products of globally subanalytic functions and logarithms of positively-valued globally subanalytic functions. Our main theorem gives uniform bounds on the decay of parameterized families of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function, assuming that the amplitude function is integrable and that the phase function satisfies a certain natural condition called the hyperplane condition. As a simple application of this theorem, we also show that any continuous, integrable, constructible function of a single variable has an integrable Fourier transform." @default.
- W2950308124 created "2019-06-27" @default.
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- W2950308124 date "2013-04-22" @default.
- W2950308124 modified "2023-09-27" @default.
- W2950308124 title "Bounding the decay of oscillatory integrals with a constructible amplitude function and a globally subanalytic phase function" @default.
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