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

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Computer Algebra in Scientific Computing (CASC 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4194))

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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.

This work was supported by State Committee for Science and Technology of the Republic of Uzbekistan, grant No. 1.1.13 and Foundation of Academy of Sciences of Uzbekistan grant no. 76-06.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, Samarkand State University, Samarkand, 703004, Uzbekistan

    Isroil A. Ikromov & Akhmadjon Soleev

Authors
  1. Isroil A. Ikromov
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  2. Akhmadjon Soleev
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Technische Universität München, Boltzmannstr. 3, 85748, Garching, Germany

    Victor G. Ganzha  & Ernst W. Mayr  & 

  2. Institute of Theoretical and Applied Mechanics, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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© 2006 Springer-Verlag Berlin Heidelberg

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Ikromov, I.A., Soleev, A. (2006). Newton Polyhedra and an Oscillation Index of Oscillatory Integrals with Convex Phases. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2006. Lecture Notes in Computer Science, vol 4194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11870814_19

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  • DOI: https://doi.org/10.1007/11870814_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45182-2

  • Online ISBN: 978-3-540-45195-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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