Synopsis
The Spectral Theory of Operators in Hilbert Space by Kurt Otto Friedrichs is a comprehensive guide to the mathematical theory of linear operators in Hilbert spaces. The book covers a wide range of topics, including the spectral theorem for bounded self-adjoint operators, the theory of unbounded operators, and the theory of compact operators. It also includes discussions on the properties of the resolvent and the spectrum of an operator, as well as applications of the theory to differential equations and quantum mechanics. The book is suitable for graduate students and researchers in mathematics, physics, and engineering who have a strong background in functional analysis and linear algebra. It is written in a clear and concise style, with numerous examples and exercises to help readers understand the material. Overall, the Spectral Theory of Operators in Hilbert Space is an essential reference for anyone interested in the theory of linear operators and its applications.The Present Lectures Intend To Provide An Introduction To The Spectral Analysis Of Self-Joint Operators Within The Framework Of Hilbert Space Theory. The Guiding Notion In This Approach Is That Of Spectral Representation. At The Same Time The Notion Of Function Of An Operator Is Emphasized. The Definition Of Hilbert Space: In Mathematics, A Hilbert Space Is A Real Or Complex Vector Space With A Positive-Definite Hermitian Form, That Is Complete Under Its Norm. Thus It Is An Inner Product Space, Which Means That It Has Notions Of Distance And Of Angle (Especially The Notion Of Orthogonality Or Perpendicularity). The Completeness Requirement Ensures That For Infinite Dimensional Hilbert Spaces The Limits Exist When Expected, Which Facilitates Various Definitions From Calculus. A Typical Example Of A Hilbert Space Is The Space Of Square Summable Sequences. Hilbert Spaces Allow Simple Geometric Concepts, Like Projection And Change Of Basis To Be Applied To Infinite Dimensional Spaces, Such As Function Spaces. They Provide A Context With Which To Formalize And Generalize The Concepts Of The Fourier Series In Terms Of Arbitrary Orthogonal Polynomials And Of The Fourier Transform, Which Are Central Concepts From Functional Analysis. Hilbert Spaces Are Of Crucial Importance In The Mathematical Formulation Of Quantum Mechanics.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
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