Introduction to Functional Analysis E-Book

Simone Malacrida

• Herausgeber: BookRix
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Veröffentlichungsjahr: 2023

Beschreibung

In this book, aspects of functional analysis are presented with respect to: Banach, Hilbert and Lebesgue spaces measure according to Lebesgue and Lebesgue integral operator view discrete and continuous transforms distributions and Sobolev spaces

Leseprobe

Simone Malacrida

Introduction to Functional Analysis

BookRix GmbH & Co. KG81371 Munich

Table of Contents

Table of Contents

"Introduction to Functional Analysis"

INTRODUCTION

FUNCTIONAL ANALYSIS

TRANSFORM

DISTRIBUTIONS

"Introduction to Functional Analysis"

"Introduction to Functional Analysis"

SIMONE MALACRIDA

In this book, aspects of functional analysis are presented with respect to:

Banach, Hilbert and Lebesgue spaces

measure according to Lebesgue and Lebesgue integral

operator view

discrete and continuous transforms

distributions and Sobolev spaces

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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 – FUNCTIONAL ANALYSIS

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 – TRANSFORM

Introduction and definitions

Fourier integral transform

Laplace integral transform

Other integral transforms

Discreet transforms

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III - DISTRIBUTIONS

Introduction and definitions

Operations

Sobolev spaces

INTRODUCTION

INTRODUCTION

Functional analysis is a branch of mathematics that is complementary to the more famous mathematical analysis.

As such, it intervenes in many aspects and in various results necessary for the resolution of mathematical and physical problems of various kinds.

Functional analysis starts from a rigorous definition of function spaces and from the study of the properties of these spaces, to then define increasingly complex operations.

With these formalisms it is possible to define transforms and distributions, two powerful methods for solving differential equations and analytic problems otherwise not known in their possible applications.

The knowledge required of the reader to understand this handbook is certainly university-level, given that, generally, the topics presented are carried out in advanced Mathematical Analysis courses (mathematical analysis 2 and mathematical analysis 3).

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