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Applications of the Theory of Generalized Solvability of Linear Equations

In: Generalized Solutions of Operator Equations and Extreme Elements

Author

Listed:
  • D. A. Klyushin

    (Kyiv National Taras Shevchenko University)

  • S. I. Lyashko

    (Kyiv National Taras Shevchenko University)

  • D. A. Nomirovskii

    (Kyiv National Taras Shevchenko University)

  • Yu. I. Petunin

    (Kyiv National Taras Shevchenko University)

  • V. V. Semenov

    (Kyiv National Taras Shevchenko University)

Abstract

Chapter 4 is the largest one. It is in a sense “barycenter” of the book. Here we consider typical examples of applications of generalized solutions in various branches of pure and applied analysis. In Sect. 4.1, 4.3, and 4.4 we prove theorems on generalized solvability of equations with Hilbert–Schmidt operators and Volterra equations of the first kind and describe their applications in the random processes estimation theory. In Sect. 4.2 the generalized solvability of linear operator equations in classic spaces of sequences is studied. In Sect. 4.5, 4.6, and 4.7 the theorems on generalized solvability of boundary value problems for parabolic and generalized wave equations are proved. Section 4.7 is devoted to discussion of theorems of Lax-Milgram kind in Banach and locally convex spaces.

Suggested Citation

  • D. A. Klyushin & S. I. Lyashko & D. A. Nomirovskii & Yu. I. Petunin & V. V. Semenov, 2012. "Applications of the Theory of Generalized Solvability of Linear Equations," Springer Optimization and Its Applications, in: Generalized Solutions of Operator Equations and Extreme Elements, edition 1, chapter 0, pages 29-101, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-0619-8_4
    DOI: 10.1007/978-1-4614-0619-8_4
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