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Newton Polyhedra and an Oscillation Index of Oscillatory Integrals with Convex Phases

  • Isroil A. Ikromov
  • Akhmadjon Soleev
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4194)

Abstract

In this paper we obtain an analog of Schultz decomposition for arbitrary convex smooth functions. We prove existence of adapted coordinate systems for analytic convex functions. We show that the oscillation index of oscillatory integrals with analytic phases is defined by the distance between Newton polyhedron constructed in adapted coordinate systems and the origin.

Keywords

Convex Function Polynomial Function Phase Function Remainder Term Oscillatory Integral 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Isroil A. Ikromov
    • 1
  • Akhmadjon Soleev
    • 1
  1. 1.Department of MathematicsSamarkand State UniversityUzbekistan

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