УслОВИЕ ОРгАНИЧЕННО стИ ОсцИлльцИОННых И НтЕгРАлОВ с кУБИЧЕскИМ МНОгОЧл ЕНОМ

Abstract

In this paper we prove that for a real finite function f(x)∃H_1,2 (Hölder's class), the generalized solution of the Cauchy problem for the Schrödinger type equation

$$\left\{ {\begin{array}{*{20}c} {D_t \psi = (\alpha D_x^3 + \beta D_x^2 + \gamma D_x )\psi ,} \\ {\psi (x,0) = f(x),} \\ \end{array} } \right.$$

where α, Β, γ∃R, is bounded on an arbitrary compact set of points (t, x)∃R ². The solution is given for the corresponding oscillatory integral.