Only one of generalized gradients can be elliptic

Jerzy Kalina; Antoni Pierzchalski; Paweł Walczak

Annales Polonici Mathematici (1997)

  • Volume: 67, Issue: 2, page 111-120
  • ISSN: 0066-2216

Abstract

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Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.

How to cite

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Jerzy Kalina, Antoni Pierzchalski, and Paweł Walczak. "Only one of generalized gradients can be elliptic." Annales Polonici Mathematici 67.2 (1997): 111-120. <http://eudml.org/doc/270175>.

@article{JerzyKalina1997,
abstract = {Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.},
author = {Jerzy Kalina, Antoni Pierzchalski, Paweł Walczak},
journal = {Annales Polonici Mathematici},
keywords = {connection; group representation; Young diagram; elliptic operator; generalized gradient; irreducible -invariant subspace; Young diagrams},
language = {eng},
number = {2},
pages = {111-120},
title = {Only one of generalized gradients can be elliptic},
url = {http://eudml.org/doc/270175},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Jerzy Kalina
AU - Antoni Pierzchalski
AU - Paweł Walczak
TI - Only one of generalized gradients can be elliptic
JO - Annales Polonici Mathematici
PY - 1997
VL - 67
IS - 2
SP - 111
EP - 120
AB - Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
LA - eng
KW - connection; group representation; Young diagram; elliptic operator; generalized gradient; irreducible -invariant subspace; Young diagrams
UR - http://eudml.org/doc/270175
ER -

References

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  1. [P] B. Ørsted and A. Pierzchalski, The Ahlfors Laplacian on a Riemannian manifold, in: Constantin Carathéodory: An International Tribute, World Sci., Singapore, 1991, 1020-1048. Zbl0746.53012
  2. [P] A. Pierzchalski, Ricci curvature and quasiconformal deformations of a Riemannian manifold, Manuscripta Math. 66 (1989), 113-127. Zbl0698.53021
  3. [SW] E. M. Stein and G. Weiss, Generalization of the Cauchy-Riemann equations and representation of the notation group, Amer. J. Math. 90 (1968), 163-197. 
  4. [We] H. Weyl, The Classical Groups, Princeton Univ. Press, Princeton, 1946. 

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