4 papers
math.CA2026
Fourier decay and Sobolev smoothing for weighted hypersurface measures in
Michael Greenblatt
We consider local hypersurface measures in whose density is allowed to have a weight function constructed from real analytic functions in a broad sense. We prove $L…
math.CA2024
Oscillatory integrals and weighted gradient flows
Michael Greenblatt
We investigate estimating scalar oscillatory integrals by integrating by parts in directions based on , where is the…
math.CA2024
Convexity, Fourier transforms, and lattice point discrepancy
Michael Greenblatt
In a well-known paper by Bruna, Nagel and Wainger [BNW], Fourier transform decay estimates were proved for smooth hypersurfaces of finite line type bounding a convex domain. In thi…
math.CA2024
A method for bounding oscillatory integrals in terms of non-oscillatory integrals
Michael Greenblatt
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an app…