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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 2, Pages 127–154 (Mi izv329)  

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

The index of Fourier integral operators on manifolds with conical singularities

V. E. Nazaikinskiia, B.-W. Schulzeb, B. Yu. Sternina

a M. V. Lomonosov Moscow State University
b University of Potsdam

Abstract: We describe homogeneous canonical transformations of the cotangent bundle of a manifold with conical singular points and compute the index of an elliptic Fourier integral operator obtained by the quantization of such a transformation. The answer involves the index of an elliptic Fourier integral operator on a smooth manifold and the residues of the conormal symbol.

DOI: https://doi.org/10.4213/im329

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English version:
Izvestiya: Mathematics, 2001, 65:2, 329–355

Bibliographic databases:

MSC: Primary 58G10, 58G12; Secondary 47A53, 47B25, 81Q60
Received: 30.10.1998

Citation: V. E. Nazaikinskii, B. Schulze, B. Yu. Sternin, “The index of Fourier integral operators on manifolds with conical singularities”, Izv. RAN. Ser. Mat., 65:2 (2001), 127–154; Izv. Math., 65:2 (2001), 329–355

Citation in format AMSBIB
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\by V.~E.~Nazaikinskii, B.~Schulze, B.~Yu.~Sternin
\paper The index of Fourier integral operators on manifolds with conical singularities
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 2
\pages 127--154
\mathnet{http://mi.mathnet.ru/izv329}
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1842842}
\zmath{https://zbmath.org/?q=an:1004.58015}
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\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 2
\pages 329--355
\crossref{https://doi.org/10.1070/im2001v065n02ABEH000329}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33747023908}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Battisti U., Coriasco S., Schrohe E., “Fourier Integral Operators and the Index of Symplectomorphisms on Manifolds With Boundary”, J. Funct. Anal., 269:11 (2015), 3528–3574  crossref  mathscinet  zmath  isi  elib  scopus
    2. Lescure J.-M., Vassout S., “Fourier Integral Operators on Lie Groupoids”, Adv. Math., 320 (2017), 391–450  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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