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Functional analysisan introductory c...

Ovchinnikov, Sergei.

Functional analysisan introductory course /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Functional analysisby Sergei Ovchinnikov.
其他題名:	an introductory course /
作者:	Ovchinnikov, Sergei.
出版者:	Cham :Springer International Publishing :2018.
面頁冊數:	xii, 205 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Functional analysis.
電子資源:	http://dx.doi.org/10.1007/978-3-319-91512-8
ISBN:	9783319915128$q(electronic bk.)

Functional analysisan introductory course /
Ovchinnikov, Sergei.

Functional analysisan introductory course /[electronic resource] :by Sergei Ovchinnikov. - Cham :Springer International Publishing :2018. - xii, 205 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Preface -- 1. Preliminaries -- 2. Metric Spaces -- 3. Special Spaces -- 4. Normed Spaces -- 5. Linear Functionals -- 6. Fundamental Theorems -- 7. Hilbert Spaces -- A. Hilbert Spaces L2(J) -- References -- Index.

This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Bounded Theory, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.

ISBN: 9783319915128$q(electronic bk.)

Standard No.: 10.1007/978-3-319-91512-8doiSubjects--Topical Terms:

200585
Functional analysis.

LC Class. No.: QA320

Dewey Class. No.: 515.7

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520 $a This concise text provides a gentle introduction to functional analysis. Chapters cover essential topics such as special spaces, normed spaces, linear functionals, and Hilbert spaces. Numerous examples and counterexamples aid in the understanding of key concepts, while exercises at the end of each chapter provide ample opportunities for practice with the material. Proofs of theorems such as the Uniform Bounded Theory, the Open Mapping Theorem, and the Closed Graph Theorem are worked through step-by-step, providing an accessible avenue to understanding these important results. The prerequisites for this book are linear algebra and elementary real analysis, with two introductory chapters providing an overview of material necessary for the subsequent text. Functional Analysis offers an elementary approach ideal for the upper-undergraduate or beginning graduate student. Primarily intended for a one-semester introductory course, this text is also a perfect resource for independent study or as the basis for a reading course.
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