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Annali di Matematica Pura ed Applicata

, Volume 92, Issue 1, pp 23–28 | Cite as

Remarks on an inequality of Schulenberger and Wilcox

  • Leonard Sarason
Article

Summary

J. R. Schulenberger and C. H. Wilcox[1], [2], have proven a coerciveness inequality for a class of nonelliptic first-order partial differential operators of the form Λ = =E −1 AjDj, where Aj (j=1, ..., n) is a constant m × m Hermitian matrix, E=E(x) is uniformly positive definite, bounded, and uniformly differentiable Hermitian m × m matrix, and where the symbol Λ(p, x)=E(x) −1 Ajpj has constant rank for all p ε Rn − {0} and x ε Rn. They prove coerciveness on N(Λ), the orthogonal complement of the null space N(Λ) relative to the inner product
$$\left\langle {u, v} \right\rangle = \int\limits_{R^n } {u(x) \cdot E(x)v(x)dx} $$
. Their proof is rather long, a simpler and shorter proof is given here. This proof leads naturally to a generalization of their results to the case where the Aj's need not be Hermitian.

Keywords

Differential Operator Null Space Orthogonal Complement Short Proof Hermitian Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [1]
    J. R. Schulenberger -C. H. Wilcox,Coerciveness inequalities for nonelliptic systems of partial differential equations, Ann. Mat. Pura Appl.,87 (to appear, 1971).Google Scholar
  2. [2]
    J. R. Schulenberger -C. H. Wilcox,A coerciveness inequality for a class of nonelliptic operators of constant deficit, Technical Summary Report no. 8, Department of Mathematics, University of Denver (October 1970).Google Scholar

Copyright information

© Nicola Zanichelli Editore 1972

Authors and Affiliations

  • Leonard Sarason
    • 1
  1. 1.SeattleU.S.A.

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