Michael Greenblatt
Published 2007-09-16, updated 2008-09-21Version 2
The elementary resolution of singularities algorithm of the author's earlier paper (math.CA/0609217) is developed further, replacing the quasibump functions in the blown up coordinates with the characteristic function of a rectangle times a smooth function. Such functions are easier to deal with, and as application the existence of asymptotic expansions for oscillatory integrals and related objects is given an elementary proof. In addition, some more detailed information about these expansions is given.
Comments: 23 pages, v2 new title and a few minor changes
On oscillatory integrals associated to phase functions with degenerate singular points
An elementary proof of the existence and uniqueness of solutions to an initial value problem
An elementary proof of the meromorphy of the integral of f^z for real-analytic f
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