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Mat. Sb., 2005, Volume 196, Number 9, Pages 23–58 (Mi msb1419)  

This article is cited in 7 scientific papers (total in 7 papers)

On the index of elliptic operators on manifolds with edges

V. E. Nazaikinskiia, A. Yu. Savinb, B. Yu. Sterninb, B.-W. Schulzec

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b Independent University of Moscow
c University of Potsdam

Abstract: Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables.

DOI: https://doi.org/10.4213/sm1419

Full text: PDF file (506 kB)
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English version:
Sbornik: Mathematics, 2005, 196:9, 1271–1305

Bibliographic databases:

UDC: 517.168.5
MSC: Primary 58J05, 58J20, 58J32; Secondary 19Kxx, 19Lxx
Received: 06.10.2004

Citation: V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Mat. Sb., 196:9 (2005), 23–58; Sb. Math., 196:9 (2005), 1271–1305

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v196/i9/p23

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    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. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Homotopy classification of elliptic operators on stratified manifolds”, Izv. Math., 71:6 (2007), 1167–1192  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, “Noncommutative geometry and classification of elliptic operators”, Journal of Mathematical Sciences, 164:4 (2010), 603–636  mathnet  crossref  mathscinet  elib
    3. A. Yu. Savin, B. Yu. Sternin, “Surgery and index formulas on stratified manifolds”, Dokl. Math., 80:1 (2009), 521–524  crossref  mathscinet  zmath  isi  elib  elib
    4. Debord C., Lescure J.-M., Nistor V., “Groupoids and an index theorem for conical pseudo-manifolds”, J. Reine Angew. Math., 628 (2009), 1–35  crossref  mathscinet  zmath  isi  elib
    5. A. Yu. Savin, B. Yu. Sternin, “Index formulas for stratified manifolds”, Differ. Equ., 46:8 (2010), 1145–1156  crossref  zmath  isi  elib  elib
    6. M. V. Korovina, “Differential equations on manifolds with edge singularities in spaces with asymptotics”, Differ. Equ., 46:5 (2010), 702–710  crossref  zmath  isi  elib  elib
    7. Nistor V., “Analysis on singular spaces: Lie manifolds and operator algebras”, J. Geom. Phys., 105 (2016), 75–101  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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