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A primer of Hilbert space

Meneghin, Claudi

ISBN 10: 3862884279 / ISBN 13: 9783862884278
Published by LINCOM, 2013
New Condition: Neu Soft cover
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Claudi Meneghin MIUR (Ministero dell'Istruzione Università e Ricerca) This book deals with the very basic theory of Hilbert space. Chapter 1 deals with the fundamental theory of vector spaces. The notion of a vector space is recalled, together with related techniques. Key definitions and theorems concerning vector spaces in general and linear independence are then reviewed. In chapter 2 the notions of a inner product, normed space and metric space are examined, together with their mutual relationships. Finally, in chapter 3 the very basic tools in the theory of Hilbert space are studied, introducing the natural generalisation of the customary vector space notions to the infinite dimensional framework. In particular, the matter of expanding a vector in terms of a (not necessarily finite) orthogonal basis is introduced. Several examples, problems and exercises are proposed. Table of Contents: Chapter 1. Vector spaces: basic definitions and properties 1. Definition of a vector space 2. Examples of vector spaces 3. Linear independence and dimension of vector spaces 4. Vector space isomorphisms Chapter 2. Inner product, normed and metric spaces 1. Inner product spaces 2. Normed spaces 3. Metric spaces Chapter 3. Hilbert space 1. Main definitions 2. Examples of Hilbert spaces 3. Separable Hilbert space 4. Convergence in Hilbert space 5. Orthonormal Bases 6. Orthogonal Subspaces and Projections 7. Riesz representation theorem ISBN 9783862884278. LINCOM Textbooks in Mathematics 01.110pp. 2013.170mm x 240mm. Bookseller Inventory # B-9783862884278

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Title: A primer of Hilbert space

Publisher: LINCOM

Publication Date: 2013

Binding: Softcover

Book Condition:Neu

Dust Jacket Condition: Neu

Edition: 1. Auflage

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This book deals with the very basic theory of Hilbert space. Chapter 1 deals with the fundamental theory of vector spaces. The notion of a vector space is recalled, together with related techniques. Key definitions and theorems concerning vector spaces in general and linear independence are then reviewed. In chapter 2 the notions of a inner product, normed space and metric space are examined, together with their mutual relationships. Finally, in chapter 3 the very basic tools in the theory of Hilbert space are studied, introducing the natural generalisation of the customary vector space notions to the infinite dimensional framework. In particular, the matter of expanding a vector in terms of a (not necessarily finite) orthogonal basis is introduced. Several examples, problems and exercises are proposed. Table of Contents: Chapter 1. Vector spaces: basic definitions and properties 1. Definition of a vector space 2. Examples of vector spaces 3. Linear independence and dimension of vector spaces 4. Vector space isomorphisms Chapter 2. Inner product, normed and metric spaces 1. Inner product spaces 2. Normed spaces 3. Metric spaces Chapter 3. Hilbert space 1. Main definitions 2. Examples of Hilbert spaces 3. Separable Hilbert space 4. Convergence in Hilbert space 5. Orthonormal Bases 6. Orthogonal Subspaces and Projections 7. Riesz representation theorem

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