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Funktsional. Anal. i Prilozhen., 1976, Volume 10, Issue 3, Pages 13–38 (Mi faa2169)  

This article is cited in 20 scientific papers (total in 20 papers)

Newton polyhedra and estimation of oscillating integrals

A. N. Varchenko

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English version:
Functional Analysis and Its Applications, 1976, 10:3, 175–196

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Received: 04.02.1976

Citation: A. N. Varchenko, “Newton polyhedra and estimation of oscillating integrals”, Funktsional. Anal. i Prilozhen., 10:3 (1976), 13–38; Funct. Anal. Appl., 10:3 (1976), 175–196

Citation in format AMSBIB
\by A.~N.~Varchenko
\paper Newton polyhedra and estimation of oscillating integrals
\jour Funktsional. Anal. i Prilozhen.
\yr 1976
\vol 10
\issue 3
\pages 13--38
\jour Funct. Anal. Appl.
\yr 1976
\vol 10
\issue 3
\pages 175--196

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    This publication is cited in the following articles:
    1. V. A. Vassiliev, “Asymptotic exponential integrals, Newton's diagram, and the classification of minimal points”, Funct. Anal. Appl., 11:3 (1977), 163–172  mathnet  crossref  mathscinet  zmath
    2. A. N. Varchenko, “A formula for the ranks of the homology groups of the boundary of an isolated singularity of a surface in $\mathbb{C}^3$ and the Newton diagram”, Funct. Anal. Appl., 13:1 (1979), 52–53  mathnet  crossref  mathscinet  zmath
    3. V. A. Vassiliev, “Asymptotic behavior of exponential integrals in the complex domain”, Funct. Anal. Appl., 13:4 (1979), 239–247  mathnet  crossref  mathscinet  zmath
    4. A. N. Varchenko, “Hodge properties of Gauss–Manin connectivities”, Funct. Anal. Appl., 14:1 (1980), 36–37  mathnet  crossref  mathscinet  zmath
    5. A. N. Varchenko, “Asymptotic Hodge structure in the vanishing cohomology”, Math. USSR-Izv., 18:3 (1982), 469–512  mathnet  crossref  mathscinet  zmath
    6. A. N. Varchenko, “The complex exponent of a singularity does not change along strata $\mu=\mathrm{const}$”, Funct. Anal. Appl., 16:1 (1982), 1–9  mathnet  crossref  mathscinet  zmath  isi
    7. V. P. Maslov, “Non-standard characteristics in asymptotic problems”, Russian Math. Surveys, 38:6 (1983), 1–42  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. V. I. Arnol'd, “Singularities of systems of rays”, Russian Math. Surveys, 38:2 (1983), 87–176  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. A. N. Varchenko, “Semicontinuity of the complex singularity index”, Funct. Anal. Appl., 17:4 (1983), 307–309  mathnet  crossref  mathscinet  zmath  isi
    10. A. N. Varchenko, “On the local residue and the intersection form on the vanishing cohomology”, Math. USSR-Izv., 26:1 (1986), 31–52  mathnet  crossref  mathscinet  zmath
    11. D. A. Popov, “Estimates with constants for some classes of oscillatory integrals”, Russian Math. Surveys, 52:1 (1997), 73–145  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    12. A. D. Bruno, “Self-similar solutions and power geometry”, Russian Math. Surveys, 55:1 (2000), 1–42  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. V. N. Karpushkin, “Uniform Estimates for Oscillatory Integrals and Volumes with the Varchenko Phase”, Math. Notes, 72:5 (2002), 636–640  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. I. A. Ikromov, “Damped Oscillatory Integrals and the Boundedness Problem for Maximal Operators”, Funct. Anal. Appl., 39:2 (2005), 70–74  mathnet  crossref  crossref  mathscinet  zmath
    15. I. A. Ikromov, “Damped Oscillatory Integrals and Maximal Operators”, Math. Notes, 78:6 (2005), 773–790  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. D. A. Popov, “Remarks on uniform combined estimates of oscillatory integrals with simple singularities”, Izv. Math., 72:4 (2008), 793–816  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. V. N. Karpushkin, “Some Phases of Oscillatory Integrals”, Funct. Anal. Appl., 45:2 (2011), 154–156  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. Kryukovskii A.S., Lukin D.S., Rastyagaev D.V., “Asimptotiki bystro ostsilliruyuschikh integralov v kriticheskoi tochke fazovoi funktsii na mnogoobrazii s kraem”, Nelineinyi mir, 10:10 (2012), 651–660  elib
    19. Bernd Martin, Dmitry Yu. Pochekutov, “Discriminant and singularities of logarithmic Gauss map, examples and application”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 74–85  mathnet
    20. I. A. Ikromov, S. E. Usmanov, “Ob ogranichennosti maksimalnykh operatorov, svyazannykh s giperpoverkhnostyami”, Sovremennye problemy matematiki i fiziki, SMFN, 64, no. 4, Rossiiskii universitet druzhby narodov, M., 2018, 650–681  mathnet  crossref
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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