# Analytic index formulas for elliptic corner operators

Boris Fedosov^{[1]}; Bert-Wolfgang Schulze^{[1]}; Nikolai Tarkhanov^{[1]}

- [1] Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne)

Annales de l’institut Fourier (2002)

- Volume: 52, Issue: 3, page 899-982
- ISSN: 0373-0956

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topFedosov, Boris, Schulze, Bert-Wolfgang, and Tarkhanov, Nikolai. "Analytic index formulas for elliptic corner operators." Annales de l’institut Fourier 52.3 (2002): 899-982. <http://eudml.org/doc/115999>.

@article{Fedosov2002,

abstract = {Spaces with corner singularities, locally modelled by cones with base spaces having
conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise
smooth geometry. We consider a typical case of a manifold with corners, the so-called
"edged spindle", and a natural algebra of pseudodifferential operators on it with special
degeneracy in the symbols, the "corner algebra". There are three levels of principal
symbols in the corner algebra, namely the interior, edge and corner conormal symbols. An
operator is called elliptic if all the three principal symbols are invertible. Elliptic
corner operators possess the Fredholm property in appropriate Sobolev spaces. We derive
an analytic index formula for such operators containing two terms of different nature:
the interior and corner contributions. This is a generalization of our previous index
formulas for cones and wedges and it suffers the same drawback: the contributions depend
not only on the three principal symbols as one could expect but rather on the complete
operator-valued symbol along the edge.},

affiliation = {Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne); Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne); Universität Potsdam, Institut für Mathematik, Postfach 60 15 53, 14415 Potsdam (Allemagne)},

author = {Fedosov, Boris, Schulze, Bert-Wolfgang, Tarkhanov, Nikolai},

journal = {Annales de l’institut Fourier},

keywords = {manifolds with singularities; pseudodifferential operators; elliptic operators; index; elliptic pseudodifferential operators; Fredholm index; index formula},

language = {eng},

number = {3},

pages = {899-982},

publisher = {Association des Annales de l'Institut Fourier},

title = {Analytic index formulas for elliptic corner operators},

url = {http://eudml.org/doc/115999},

volume = {52},

year = {2002},

}

TY - JOUR

AU - Fedosov, Boris

AU - Schulze, Bert-Wolfgang

AU - Tarkhanov, Nikolai

TI - Analytic index formulas for elliptic corner operators

JO - Annales de l’institut Fourier

PY - 2002

PB - Association des Annales de l'Institut Fourier

VL - 52

IS - 3

SP - 899

EP - 982

AB - Spaces with corner singularities, locally modelled by cones with base spaces having
conical singularities, belong to the hierarchy of (pseudo-) manifolds with piecewise
smooth geometry. We consider a typical case of a manifold with corners, the so-called
"edged spindle", and a natural algebra of pseudodifferential operators on it with special
degeneracy in the symbols, the "corner algebra". There are three levels of principal
symbols in the corner algebra, namely the interior, edge and corner conormal symbols. An
operator is called elliptic if all the three principal symbols are invertible. Elliptic
corner operators possess the Fredholm property in appropriate Sobolev spaces. We derive
an analytic index formula for such operators containing two terms of different nature:
the interior and corner contributions. This is a generalization of our previous index
formulas for cones and wedges and it suffers the same drawback: the contributions depend
not only on the three principal symbols as one could expect but rather on the complete
operator-valued symbol along the edge.

LA - eng

KW - manifolds with singularities; pseudodifferential operators; elliptic operators; index; elliptic pseudodifferential operators; Fredholm index; index formula

UR - http://eudml.org/doc/115999

ER -

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