Exercises of Functional Analysis

Table of Contents

Table of Contents

Exercises of Functional Analysis

INTRODUCTION

THEORETICAL OUTLINE

EXERCISES

Exercises of Functional Analysis

Exercises of Functional Analysis

SIMONE MALACRIDA

In this book, exercises are carried out regarding the following mathematical topics:

Banach and Hilbert spaces

operations in vector spaces

Lebesgue measure and integral.

Initial theoretical hints are also presented to make the conduct of the exercises understandable.

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 – THEORETICAL OUTLINE

Introduction and definitions

Norms and regulated spaces

Hilbert spaces

Lebesgue measure and Lebesgue integral

Lebesgue spaces

Other results of functional analysis and operative vision

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II – EXERCISES

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 17

Exercise 18

Exercise 19

Exercise 20

Exercise 21

Exercise 22

INTRODUCTION

INTRODUCTION

In this workbook, some examples of calculations related to functional analysis are carried out.

Furthermore, the main theorems used in this area of mathematics are presented.

Functional analysis completes and enriches the study of mathematical analysis by proposing new solutions and new fields of application.

In fact, without the typical setting of functional analysis, the integral transforms and distributions would not be determined.

In order to understand in more detail what is presented in the resolution of the exercises, the theoretical reference context is recalled in the first chapter.

What is exposed in this workbook is generally addressed in advanced mathematical analysis courses (analysis 3).