Introduction to Spectral Theory E-Book

Simone Malacrida

• Herausgeber: Simone Malacrida
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2022

Beschreibung

The following topics are presented in this book:
basic concepts of operator functional analysis
spectral theorem and spectral measurements
Stone's theorem and physical applications

Leseprobe

Table of Contents

"Introduction to Spectral Theory"

INTRODUCTION

BASIC CONCEPTS

SPECTRAL THEORY

PHYSICAL APPLICATIONS

"Introduction to Spectral Theory"

SIMONE MALACRIDA

The following topics are presented in this book:

basic concepts of operator functional analysis

spectral theorem and spectral measurements

Stone's theorem and physical applications

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Simone Malacrida (1977)

Engineer and writer, has worked on research, finance, energy policy and industrial plants.

ANALYTICAL INDEX

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INTRODUCTION

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I – BASIC CONCEPTS

Definitions

Spectrum classification

Riesz theorem

Functions of self-adjoint operators

Non-negative operators

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II - SPECTRAL THEORY

The spectral theorem

Spectral and integral measurements

Spectral measurement of an operator

Stone's theorem

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III - PHYSICAL APPLICATIONS

Schrodinger equation

Harmonic Oscillator

INTRODUCTION

Spectral theory is presented in this book as a separate discipline from functional analysis.

Although spectral theory can fall within the study of functional analysis at an operational level, the importance it has assumed for the resolution of many physical problems gives it a new and broader perspective.

After having mentioned the main results in the field of functional analysis (without however going into the smallest details for which reference is made to specific texts relating to the subject), the cornerstones of the spectral theory given by the spectral theorem and by the spectral measurements will be presented.

Through Stone's theorem it will be possible to apply these concepts to two real cases such as the Schrodinger equation which governs quantum mechanics and the harmonic oscillator.

As such, advanced mathematical analysis and functional analysis preconditions are necessary, certainly at an in-depth university level, in order to understand what will be presented.

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