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Funktsional. Anal. i Prilozhen., 2001, Volume 35, Issue 2, Pages 37–52 (Mi faa244)  

This article is cited in 12 scientific papers (total in 12 papers)

The Index Locality Principle in Elliptic Theory

V. E. Nazaikinskiia, B. Yu. Sterninb

a A. Ishlinsky Institite for Problems in Mechanics, Russian Academy of Sciences
b M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov–Lawson, Anghel, Teleman, Booß-Bavnbek–Wojciechowski, et al. as special cases. In conjunction with some additional conditions (like symmetry conditions), this theorem permits computing the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.

DOI: https://doi.org/10.4213/faa244

Full text: PDF file (261 kB)
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English version:
Functional Analysis and Its Applications, 2001, 35:2, 111–123

Bibliographic databases:

UDC: 517.9
Received: 21.01.2000

Citation: V. E. Nazaikinskii, B. Yu. Sternin, “The Index Locality Principle in Elliptic Theory”, Funktsional. Anal. i Prilozhen., 35:2 (2001), 37–52; Funct. Anal. Appl., 35:2 (2001), 111–123

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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. Nazaikinskii V.E., Sternin B.Y., “A remark on surgery in index theory of elliptic operators”, Jean Leray '99 Conference Proceedings - the Karlskrona Conference in Honor of Jean Leray, Mathematical Physics Studies, 24, 2003, 363  mathscinet  zmath  isi
    2. V. E. Nazaikinskii, A. Yu. Savin, B. Yu. Sternin, B.-W. Schulze, “On the index of elliptic operators on manifolds with edges”, Sb. Math., 196:9 (2005), 1271–1305  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. Nazaikinskii, VE, “Surgery and the relative index in elliptic theory”, Abstract and Applied Analysis, 2006, 98081  mathscinet  zmath  isi
    4. Harutjunjan, G, “The relative index for corner singularities”, Integral Equations and Operator Theory, 54:3 (2006), 385  crossref  mathscinet  zmath  isi
    5. Dines, N, “Mixed boundary value problems and parametrices in the edge calculus”, Bulletin Des Sciences Mathematiques, 131:4 (2007), 325  crossref  mathscinet  zmath  isi
    6. Liu, XC, “Boundary value problems in edge representation”, Mathematische Nachrichten, 280:5–6 (2007), 581  crossref  mathscinet  zmath  isi
    7. Dines N., “Ellipticity of a class of corner operators”, Pseudo-Differential Operators: Partial Differential Equations and Time-Frequency Analysis, Fields Institute Communications, 52, 2007, 131–169  mathscinet  zmath  isi
    8. Abed J., Schulze B.-W., “Operators with Corner-Degenerate Symbols”, New Developments in Pseudo-Differential Operators, Operator Theory : Advances and Applications, 189, 2009, 67–106  crossref  mathscinet  isi
    9. M. I. Katsnel'son, V. E. Nazaikinskii, “The Aharonov–Bohm effect for massless Dirac fermions and the spectral flow of Dirac-type operators with classical boundary conditions”, Theoret. and Math. Phys., 172:3 (2012), 1263–1277  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    10. Ping L., “Analysis and Development of the Locality Principle”, Frontiers in Computer Education, Advances in Intelligent and Soft Computing, 133, eds. Sambath S., Zhu E., Springer-Verlag Berlin, 2012, 211–214  crossref  isi
    11. V. E. Nazaikinskii, “Relative Index Theorem in $K$-Homology”, Funct. Anal. Appl., 49:4 (2015), 311–314  mathnet  crossref  crossref  isi  elib
    12. Nazaikinskii V.E., “on a Kk-Theoretic Counterpart of Relative Index Theorems”, Russ. J. Math. Phys., 22:3 (2015), 374–378  crossref  mathscinet  zmath  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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