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In addition to the basic theory it explains operator theory, distributions, Sobolev spaces, and many other things. The text is self-contained and includes all proofs, as well as many exercises, most of them with solutions.

Nondifferentiable Continuous Functions. We shall cover approximately the material from most of the textbook by Atiyah-MacDonald, or the first half of the textbook by Bosch. This is why very different techniques are employed when studying linear operators and operators in general in the infinite-dimensional case. These calculations react to be and love, and they really meet their special contents. Ability to solve simple problems. Another application-oriented book on Hilbert spaces suitable for a physics audience.

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1 2 What is the purpose of functional analysis

About this product Product Information This book gives an introduction to Linear Functional Analysis, which is a synthesis of algebra, topology, and analysis. Moreover, there are a number of appendices, for example on Lebesgue integration theory. A complete introduction to the subject, Linear Functional Analysis will be particularly useful to readers who want to quickly get to the key statements and who are interested in applications to differential equations.

Additional Product Features Number of Volumes. More precisely, by i , I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to i , approach ii starts out from the question "What are the most important applications? Here, one walks directly on the main road and does not wander into all the nice and interesting side roads. The present book is based on the second approach.

It is addressed to undergraduate and beginning graduate students of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems that are related to our real world and that have played an important role in the history of mathematics. The reader should sense that the theory is being developed, not simply for its own sake, but for the effective solution of concrete problems.

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Hilbert Spaces Orthogonality and the Dirichlet Principle. Hilbert Spaces and Generalized Fourier Series.