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Sectorial Forms and m-Sectorial Operators

  • Konrad Schmüdgen
Chapter
  • 4.3k Downloads
Part of the Graduate Texts in Mathematics book series (GTM, volume 265)

Abstract

Chapter 11 is concerned with nonsymmetric forms. First, the Lax–Milgram lemma for bounded coercive forms is obtained. The main results of this chapter are two form representation theorems, one for bounded coercive forms on densely and continuously embedded Hilbert spaces and another one for densely defined closed sectorial forms. The latter gives a one-to-one correspondence between densely defined closed sectorial forms and m-sectorial operators. Finally, this form representation theorem is applied to second-order elliptic differential operators.

Keywords

Formal Sector Second-order Elliptic Differential Operator Nonsymmetric Form Continuous Embedding Hilbert Space Isomorphism 
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.

References

Books

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    Agmon, S.: Lectures on Elliptic Boundary Problems. Van Nostrand, Princeton (1965) zbMATHGoogle Scholar
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    Lions, J.L., Magenes, E.: Non-Homogeneous Boundary Value Problems and Applications, vol. I. Springer-Verlag, Berlin (1972) CrossRefzbMATHGoogle Scholar
  3. [Tn]
    Tanabe, H.: Equations of Evolution. Pitman, London (1979) zbMATHGoogle Scholar

Articles

  1. [Ka]
    Kaufman, W.F.: Representing a closed operator as a quotient of continuous operators. Proc. Am. Math. Soc. 72, 531–534 (1978) CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Konrad Schmüdgen
    • 1
  1. 1.Dept. of MathematicsUniversity of LeipzigLeipzigGermany

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