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Titlebook: Applications of Functional Analysis in Engineering; J. L. Nowinski Book 1981 Springer Science+Business Media New York 1981 Finite.Hilbert

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发表于 2025-3-21 17:08:10 | 显示全部楼层 |阅读模式
期刊全称Applications of Functional Analysis in Engineering
影响因子2023J. L. Nowinski
视频videohttp://file.papertrans.cn/160/159437/159437.mp4
学科分类Mathematical Concepts and Methods in Science and Engineering
图书封面Titlebook: Applications of Functional Analysis in Engineering;  J. L. Nowinski Book 1981 Springer Science+Business Media New York 1981 Finite.Hilbert
影响因子Functional analysis owes its OrIgms to the discovery of certain striking analogies between apparently distinct disciplines of mathematics such as analysis, algebra, and geometry. At the turn of the nineteenth century, a number of observations, made sporadically over the preceding years, began to inspire systematic investigations into the common features of these three disciplines, which have developed rather independently of each other for so long. It was found that many concepts of this triad-analysis, algebra, geometry-could be incorporated into a single, but considerably more abstract, new discipline which came to be called functional analysis. In this way, many aspects of analysis and algebra acquired unexpected and pro­ found geometric meaning, while geometric methods inspired new lines of approach in analysis and algebra. A first significant step toward the unification and generalization of algebra, analysis, and geometry was taken by Hilbert in 1906, who studied the collection, later called 1 , composed of infinite sequences x = Xb X 2, ... , 2 X , ... , of numbers satisfying the condition that the sum Ik"= 1 X 2 converges. k k The collection 12 became a prototype of the cla
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Function Space,bstract space element—at this stage we choose to change our approach and concentrate on the particular class of abstract spaces known as function spaces. A . is an abstract space, the elements of which are functions or sets of functions defined in an appropriate domain.
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Bounds and Inequalities, is both theoretically defensible and practically unavoidable. This fact, however, does not absolve us from the obligation of estimating the error of the approximation solution, either by a direct computation or, more often, by finding the so-called .. In this chapter, we devote our attention to the
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The Method of the Hypercircle,ranslates the analytical content of a problem into the language of function space, thereafter studying the problem in geometric terms. Although the fundamental relations of the method turn out to follow almost directly from the Cauchy-Schwarz and Bessel inequalities, the remarkable pictorial merits
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