RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 4, Pages 173–196 (Mi izv1141)  

This article is cited in 2 scientific papers (total in 2 papers)

Remarks on uniform combined estimates of oscillatory integrals with simple singularities

D. A. Popov

A. N. Belozersky Institute of Physico-Chemical Biology, M. V. Lomonosov Moscow State University

Abstract: We consider the problem of constructing asymptotically exact (for $\Omega\gg 1$) uniform (with respect to parameters $t=(t_1,t_2,…,t_m)$) estimates for oscillatory integrals containing a large parameter $\Omega$. We suggest a possible multidimensional analogue of Vinogradov's well-known estimate for one-dimensional integrals. Based on this suggestion, we estimate the integrals with singularities of type $A_k$, $D_4^{\pm}$ (in Arnold's classification) and use the special case of $D_5^\pm$ to discuss the possibility of generalizing our results.

DOI: https://doi.org/10.4213/im1141

Full text: PDF file (583 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2008, 72:4, 793–816

Bibliographic databases:

UDC: 517.3
MSC: 42B20, 58C25, 58J37
Received: 12.07.2006
Revised: 20.09.2007

Citation: D. A. Popov, “Remarks on uniform combined estimates of oscillatory integrals with simple singularities”, Izv. RAN. Ser. Mat., 72:4 (2008), 173–196; Izv. Math., 72:4 (2008), 793–816

Citation in format AMSBIB
\Bibitem{Pop08}
\by D.~A.~Popov
\paper Remarks on uniform combined estimates of oscillatory integrals
with simple singularities
\jour Izv. RAN. Ser. Mat.
\yr 2008
\vol 72
\issue 4
\pages 173--196
\mathnet{http://mi.mathnet.ru/izv1141}
\crossref{https://doi.org/10.4213/im1141}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2452238}
\zmath{https://zbmath.org/?q=an:1155.42004}
\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2008IzMat..72..793P}
\elib{https://elibrary.ru/item.asp?id=11161435}
\transl
\jour Izv. Math.
\yr 2008
\vol 72
\issue 4
\pages 793--816
\crossref{https://doi.org/10.1070/IM2008v072n04ABEH002419}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000259374600008}
\elib{https://elibrary.ru/item.asp?id=13579718}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-53349107383}


Linking options:
  • http://mi.mathnet.ru/eng/izv1141
  • https://doi.org/10.4213/im1141
  • http://mi.mathnet.ru/eng/izv/v72/i4/p173

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Akbar R. Safarov, “On invariant estimates for oscillatory integrals with polynomial phase”, Zhurn. SFU. Ser. Matem. i fiz., 9:1 (2016), 102–107  mathnet  crossref
    2. A. R. Safarov, “Invariant Estimates of Two-Dimensional Oscillatory Integrals”, Math. Notes, 104:2 (2018), 293–302  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:369
    Full text:139
    References:57
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021