Titlebook: Introductory Functional Analysis; With Applications to B. Daya Reddy Textbook 1998 Springer Science+Business Media New York 1998 Algebra.ca

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Sets of functions and Lebesgue integrationas Hilbert spaces. In the development of this theory it is not necessary to appeal to the precise character of a set: the basic axioms, and the theorems that follow from these axioms, apply equally to sets whose members are numbers or matrices or functions. Before embarking on the task of describing

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Vector spaces, normed, and inner product spacesup a nontrivial theory, let alone be of use in concrete applications. Additional structure has to be added: we agree to add together vectors using the parallelogram law, and we define various forms of multiplication of vectors, for example, the scalar (dot) product and the vector (cross) product. On

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Linear operatorsndamental concept in functional analysis, namely, that of a mapping or operator from one space to another. At the most primitive level one requires only two sets in order to define an operator from one of them to the other, and these sets need not have any algebraic or topological structure for the

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Distributions and Sobolev spaces introduction to functional analysis. Given the problem of finding a function . that satisfies a partial differential equation and one or more boundary conditions, it is clearly of great value to know beforehand whether such a solution exists and, if so, whether it is unique, and finally how smooth

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Elliptic boundary value problemsalue problems. Section 8.1 sets the stage by introducing a range of problems involving differential equations; we saw some examples in the Introduction, and here the opportunity is taken to introduce a few more.

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Approximate methods of solutionre we can quite justifiably ask: how does one actually obtain solutions? The answer is rather disappointing, unfortunately; except for problems involving very simple PDEs and geometries, it is quite impossible, using existing methods, to obtain exact solutions to most BVPs in either the conventional