Remarks on uniform combined estimates of oscillatory integrals with simple singularitiesстатья
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Дата последнего поиска статьи во внешних источниках: 14 сентября 2013 г.
Аннотация:We consider the problem of constructing asymptotically exact (for Omega >> 1) uniform (with respect to parameters t = (t(1), t(2), ... , t(m))) estimates for oscillatory integrals containing a large parameter Omega. We suggest a possible multidimensional analogue of Vinogradov's well-known estimate for one-dimensional integrals. Based on this suggestion, we estimate the integrals with singularities of type A(k), D(4)(+/-) (in Arnold's classification and use the special case of D(5)(+/-) to discuss the possibility of generalizing our results.