Overdetermined Equations

  • S. G. Krein


Sometimes we have to deal with equations (A) such that one can see from their structure immediately that they cannot be solved for all y ∈ F. For example, this happens if there is a closed operator Φ, acting from F into another Banach space G, and such that ΦA = 0. Then equation Ax = y can be solved only for y ∈ N(Φ). Relative to a given pair of spaces E and F, an equation which can be solved only when the right-hand side is contained in a subspace F, of F, must be naturally considered as overdetermined.


Banach Space Homogeneous Equation Orthogonal Complement Closed Operator Unique Solvability 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Boston, Inc. 1982

Authors and Affiliations

  • S. G. Krein
    • 1
  1. 1.Department of MathematicsVoronezh UniversityVoronezhUSSR

Personalised recommendations