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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 1, Pages 91–93
DOI: https://doi.org/10.4213/faa2937 (Mi faa2937) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Brief communications

Pointwise van der Corput Lemma for Functions of Several Variables

M. V. Ruzhanskii

Imperial College London
Full-text PDF (127 kB) Citations (10)
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DOI: https://doi.org/10.4213/faa2937
Abstract: A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional decay estimate. The obtained estimates are uniform with respect to parameters on which the phases and amplitudes may depend.
Keywords: van der Corput lemma, oscillatory integral, asymptotic estimate.
Received: 13.04.2007
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 1, Pages 75–77
DOI: https://doi.org/10.1007/s10688-009-0010-5
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
Citation: M. V. Ruzhanskii, “Pointwise van der Corput Lemma for Functions of Several Variables”, Funktsional. Anal. i Prilozhen., 43:1 (2009), 91–93; Funct. Anal. Appl., 43:1 (2009), 75–77
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa2937
  • https://doi.org/10.4213/faa2937
  • https://www.mathnet.ru/eng/faa/v43/i1/p91
    • This publication is cited in the following 10 articles:
    1. Akbar R. Safarov, Ulugbek A. Ibragimov, “Oscillatory integrals for Mittag–Leffler functions”, Zhurn. SFU. Ser. Matem. i fiz., 17:4 (2024), 488–496  mathnet
    2. Isroil A. Ikromov, Michael Ruzhansky, Akbar R. Safarov, “Oscillatory integrals for Mittag-Leffler functions with two variables”, Comptes Rendus. Mathématique, 362:G7 (2024), 789  crossref
    3. Michael Ruzhansky, Akbar R. Safarov, Gafurjan A. Khasanov, “Uniform estimates for oscillatory integrals with homogeneous polynomial phases of degree 4”, Anal.Math.Phys., 12:6 (2022)  crossref
    4. Jinping Zhuge, “Homogenization and boundary layers in domains of finite type”, Communications in Partial Differential Equations, 43:4 (2018), 549  crossref
    5. Tokio Matsuyama, Michael Ruzhansky, “Scattering for strictly hyperbolic systems with time‐dependent coefficients”, Mathematische Nachrichten, 286:11-12 (2013), 1191  crossref
    6. Jens Wirth, Springer Proceedings in Mathematics & Statistics, 44, Progress in Partial Differential Equations, 2013, 367  crossref
    7. Ruzhansky M., “Multidimensional decay in the van der Corput lemma”, Studia Math., 208:1 (2012), 1–10  crossref  mathscinet  zmath  isi
    8. Ruzhansky M., Wirth J., “Dispersive estimates for hyperbolic systems with time-dependent coefficients”, J. Differential Equations, 251:4-5 (2011), 941–969  crossref  mathscinet  zmath  adsnasa  isi
    9. Matsuyama T., Ruzhansky M., “Asymptotic integration and dispersion for hyperbolic equations”, Adv. Differential Equations, 15:7-8 (2010), 721–756  mathscinet  zmath  isi
    10. G. M. Gubreev, A. A. Tarasenko, “Spectral decomposition of model operators in de Branges spaces”, Sb. Math., 201:11 (2010), 1599–1634  mathnet  mathnet  crossref  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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