Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena

Details Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena Resolution of singularities, asymptotic expansions of oscillatory integrals, and related phenomena

2007-09-16

arxiv.org/abs/0709.2496v2

Mathematics

Classical Analysis and ODEs

23 pages, v2 new title and a few minor changes

Scientific paper

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.

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