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A primer on Hilbert space theory[electronic resource] :linear spaces, topological spaces, metric spaces, normed spaces, and topological groups /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
杜威分類號:	515.733
書名/作者:	A primer on Hilbert space theory : linear spaces, topological spaces, metric spaces, normed spaces, and topological groups // by Carlo Alabiso, Ittay Weiss.
作者:	Alabiso, Carlo.
其他作者:	Weiss, Ittay.
出版者:	Cham : : Springer International Publishing :, 2015.
面頁冊數:	xvii, 255 p. : : ill., digital ;; 24 cm.
Contained By:	Springer eBooks
標題:	Hilbert space.
標題:	Topological spaces.
標題:	Metric spaces.
標題:	Normed linear spaces.
標題:	Physics.
標題:	Mathematical Methods in Physics.
標題:	Functional Analysis.
標題:	Algebraic Topology.
ISBN:	9783319037134 (electronic bk.)
ISBN:	9783319037127 (paper)
內容註:	1 Introduction and Preliminaries -- 2 Linear Spaces -- 3 Topological Spaces -- 4 Metric Spaces -- 5 Normed Spaces -- 6 Topological Groups -- 7 Solved Problems.
摘要、提要註:	This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.
電子資源:	http://dx.doi.org/10.1007/978-3-319-03713-4

A primer on Hilbert space theory[electronic resource] :linear spaces, topological spaces, metric spaces, normed spaces, and topological groups /
Alabiso, Carlo.

A primer on Hilbert space theorylinear spaces, topological spaces, metric spaces, normed spaces, and topological groups /[electronic resource] :by Carlo Alabiso, Ittay Weiss. - Cham :Springer International Publishing :2015. - xvii, 255 p. :ill., digital ;24 cm. - UNITEXT for physics,2198-7882. - UNITEXT for physics..

1 Introduction and Preliminaries -- 2 Linear Spaces -- 3 Topological Spaces -- 4 Metric Spaces -- 5 Normed Spaces -- 6 Topological Groups -- 7 Solved Problems.

This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics.

ISBN: 9783319037134 (electronic bk.)

Standard No.: 10.1007/978-3-319-03713-4doiSubjects--Topical Terms:

465745
Hilbert space.

LC Class. No.: QA322.4

Dewey Class. No.: 515.733

A primer on Hilbert space theory[electronic resource] :linear spaces, topological spaces, metric spaces, normed spaces, and topological groups /
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