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Titlebook: Variational Methods in Mathematics, Science and Engineering; Karel Rektorys Book 1977 Karel Rektorys 1977 Mathematica.applied mathematics.

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signed, in the first place, for specialists in the fields of theoretical engineering and science. However, it was my aim that the book should be of interest to mathematicians as well. I have been well aware what an ungrateful task it may be to write a book of the present type, and what problems such an effort978-94-011-6452-8978-94-011-6450-4
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The Space In the Hilbert space ., let a linear set . dense in . be given and on it an operator . which maps . into. and which is positive definite on ., thus symmetric on. and such that there exists a constant C > 0 so that
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The Galerkin MethodConsider a separable Hilbert space . and a set . of its elements which is dense in .. According to Theorem 6.18, p. 79, if for some element . ∈ ..then it follows that . = 0 in .. Let now.be a base in .. The assertion is that if (., ϕ.) = 0 holds for all . = 1,2,… then again . = 0 in .. Briefly written,
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Summary of Chapters 9 to 16The contents of Part II, i.e., of Chapters 9–16, are relatively rich. It will be of use to summarize the main results of Part II in this chapter and to enable the reader a better orientation in its subject matter in this way.
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