Gravitation and Cosmology.
Vol. 15.
2009.
P. 213-219

The elliptic theory of pseudodifferential operators (PDOs) on stratified manifolds with any stratification length, is proved. Any elliptic operator is Fredholm. A set of symbols on strata is the symbol of some elliptic operator if and only if the given symbols satisfy a certain condition, called the compatibility condition. In this situation, the principal symbol of a pseudodifferential operator is the set of symbols on strata. Each of these symbols is an operator-valued function defined on the cotangent bundle of the corresponding open stratum. The ellipticity condition on an operator means that the principal symbol must be invertible.

Authors

Journal

Number of issue

1

Language

English

Pages

521-524

Status

Published

Link

Volume

80

Year

2009

Organizations

^{1}Independent University of Moscow, Bol'shoi Vlas'evskii per. 11, Moscow 119002, Russian Federation^{2}Peoples' Friendship University, ul. Miklukho-Maklaya 6, Moscow 117198, Russian Federation

Keywords

Compatibility conditions; Elliptic operator; Fredholm; Index formula; Operator-valued functions; Pseudo-differential operator; Mathematical operators; Geometry

Date of creation

19.10.2018

Date of change

19.10.2018

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Gravitation and Cosmology.
Vol. 15.
2009.
P. 213-219

Gravitation and Cosmology.
Vol. 15.
2009.
P. 241-246