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The Major Definitions, Concepts and Auxiliary Facts

  • D. A. Klyushin
  • S. I. Lyashko
  • D. A. Nomirovskii
  • Yu. I. Petunin
  • V. V. Semenov
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 55)

Abstract

In Chap. 1 we give major definitions, concepts and auxiliary facts concerning the theory of generalized solutions, namely: linear vector space, dual pair, linear functional, continuous functional, conjugate space, algebraically conjugate space, second conjugate space, bilinear form, linear operator, injective operator, bijective operator, surjective operator, adjoint operator, algebraically adjoint operator, intermediate space, topological space, linear normed space, embedding, dense embedding, natural embedding, strong topology, weak topology, bounded set, subdifferential, Banach space, Sobolev space, neighborhood.

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • D. A. Klyushin
    • 1
  • S. I. Lyashko
    • 1
  • D. A. Nomirovskii
    • 1
  • Yu. I. Petunin
    • 1
  • V. V. Semenov
    • 1
  1. 1.Department of CyberneticsKyiv National Taras Shevchenko UniversityKyivUkraine

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