From Euclidean to Hilbert spaces : introduction to functional analysis and its applications / Edoardo Provenzi.

Format:

Book

Author/Creator:

Provenzi, Edoardo, author.

Language:

English

Subjects (All):

Functional analysis.

Physical Description:

1 online resource (350 pages)

Place of Publication:

London, England ; Hoboken, New Jersey : ISTE : Wiley, [2021]

Summary:

From Euclidian to Hilbert Spaces analyzes the transition from finite dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a notion that can sometimes be difficult for non-specialists to grasp. The focus is on the parallels and differences between the properties of the finite and infinite dimensions, noting the fundamental importance of coherence between the algebraic and topological structure, which makes Hilbert spaces the infinite-dimensional objects most closely related to Euclidian spaces. The common thread of this book is the Fourier transform, which is examined starting from the discrete Fourier transform (DFT), along with its applications in signal and image processing, passing through the Fourier series and finishing with the use of the Fourier transform to solve differential equations. The geometric structure of Hilbert spaces and the most significant properties of bounded linear operators in these spaces are also covered extensively. The theorems are presented with detailed proofs as well as meticulously explained exercises and solutions, with the aim of illustrating the variety of applications of the theoretical results.

Contents:

Inner Product Spaces (Pre-Hilbert)

The Discrete Fourier Transform and its Applications to Signal and Image Processing

Lebesgue's Measure and Integration Theory

Banach Spaces and Hilbert Spaces

The Geometric Structure of Hilbert Spaces

Bounded Linear Operators in Hilbert Spaces

Quotient Space

The Transpose (or Dual)of a Linear Operator

Uniform, Strong and Weak Convergence.

Notes:

Description based on print version record.

Includes bibliographical references and index.

ISBN:

9781119851295

1119851297

9781119851318

1119851319

9781119851301

1119851300

OCLC:

1263023789