eBook - ePub
From Euclidean to Hilbert Spaces
Introduction to Functional Analysis and its Applications
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
From Euclidean to Hilbert Spaces
Introduction to Functional Analysis and its Applications
About this book
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.
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.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access From Euclidean to Hilbert Spaces by Edoardo Provenzi in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Cover
- Table of Contents
- Dedication
- Title Page
- Copyright
- Preface
- 1 Inner Product Spaces (Pre-Hilbert)
- 2 The Discrete Fourier Transform and its Applications to Signal and Image Processing
- 3 Lebesgue’s Measure and Integration Theory
- 4 Banach Spaces and Hilbert Spaces
- 5 The Geometric Structure of Hilbert Spaces
- 6 Bounded Linear Operators in Hilbert Spaces
- Appendix 1: Quotient Space
- Appendix 2: The Transpose (or Dual) of a Linear Operator
- Appendix 3: Uniform, Strong and Weak Convergence
- References
- Index
- End User License Agreement