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Mat. Tr., 2005, Volume 8, Number 1, Pages 176–201 (Mi mt59)  

This article is cited in 8 scientific papers (total in 8 papers)

Geometric Symbol Calculus for Pseudodifferential Operators. II

V. A. Sharafutdinov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: A connection on a manifold allows us to define the full symbol of a pseudodifferential operator in an invariant way. The latter is called the geometric symbol to distinguish it from the coordinate-wise symbol. The traditional calculus is developed for geometric symbols: an expression of the geometric symbol through the coordinate-wise symbol, formulas for the geometric symbol of the product of two operators, and of the dual operator. The second part considers operators on vector bundles.

Key words: pseudodifferential operator, connection on a manifold, covariant derivative.

Full text: PDF file (1844 kB)
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English version:
Siberian Advances in Mathematics, 2005, 15:4, 71–95

Bibliographic databases:

UDC: 517.98
Received: 09.07.2003

Citation: V. A. Sharafutdinov, “Geometric Symbol Calculus for Pseudodifferential Operators. II”, Mat. Tr., 8:1 (2005), 176–201; Siberian Adv. Math., 15:4 (2005), 71–95

Citation in format AMSBIB
\Bibitem{Sha05}
\by V.~A.~Sharafutdinov
\paper Geometric Symbol Calculus for Pseudodifferential Operators.~II
\jour Mat. Tr.
\yr 2005
\vol 8
\issue 1
\pages 176--201
\mathnet{http://mi.mathnet.ru/mt59}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1955026}
\zmath{https://zbmath.org/?q=an:1082.58025}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 4
\pages 71--95


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    This publication is cited in the following articles:
    1. V. V. Dzhepko, Yu. G. Nikonorov, “The Double Exponential Map on Spaces of Constant Curvature”, Siberian Adv. Math., 18:1 (2008), 21–29  mathnet  crossref  mathscinet
    2. A. V. Gavrilov, “The Leibniz formula for the covariant derivative and some of its applications”, Siberian Adv. Math., 22:2 (2012), 80–94  mathnet  crossref  mathscinet
    3. Hansen S., “Rayleigh-Type Surface Quasimodes in General Linear Elasticity”, Analysis & PDE, 4:3 (2011), 461–497  crossref  mathscinet  zmath  isi  scopus
    4. A. V. Gavrilov, “The affine connection in the normal coordinates”, Siberian Adv. Math., 23:1 (2013), 1–19  mathnet  crossref  mathscinet  elib
    5. Yu. G. Nikonorov, “Double exponential map on symmetric spaces”, Siberian Adv. Math., 23:3 (2013), 210–218  mathnet  crossref  mathscinet  elib
    6. Hansen S., Hilgert J., Schroeder M., “Patterson-Sullivan Distributions in Higher Rank”, Math. Z., 272:1-2 (2012), 607–643  crossref  mathscinet  zmath  isi  scopus
    7. Freund S., Teufel S., “Peierls Substitution For Magnetic Bloch Bands”, Anal. PDE, 9:4 (2016), 773–811  crossref  mathscinet  zmath  isi  scopus
    8. Pali N., “Exact Fourier Inversion Formula Over Manifolds”, J. Pseudo-Differ. Oper. Appl., 8:4 (2017), 623–628  crossref  mathscinet  zmath  isi  scopus
  • Математические труды Siberian Advances in Mathematics
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