A Priori Estimates for Linear Continuous Operators

D. A. Klyushin (), S. I. Lyashko (), D. A. Nomirovskii (), Yu. I. Petunin () and V. V. Semenov ()
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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

Chapter Chapter 3 in Generalized Solutions of Operator Equations and Extreme Elements, 2012, pp 17-27 from Springer

Abstract: Abstract In Chap. 3 the operator equations with continuous linear injective operator which acts in linear normed spaces are considered in greater detail. The spaces of strong and weak generalized solutions defined in previous chapter do not allow any constructive description in general case. In Sects. 3.1 and 3.2 we develop a variant of the theory, using the duality techniques, that is more useful for concrete applications. In Sects. 3.3 and 3.4 we study the alternative constructive approach to general solvability, based on the duality techniques.

Keywords: Priori Estimates; Injective Continuous Linear Operator; Generalized Solvability; Constructive Description; Duality Techniques (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-0619-8_3

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