Edoardo Provenzi
From Euclidean to Hilbert Spaces: Introduction to Functional Analysis and its Applications
From Euclidean to Hilbert Spaces: Introduction to Functional Analysis and its Applications
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Excellent- More about From Euclidean to Hilbert Spaces: Introduction to Functional Analysis and its Applications
The book From Euclidian to Hilbert Spaces explores the transition from finite-dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, emphasizing coherence between algebraic and topological structure. It covers the Fourier transform, geometric structure, and bounded linear operators, with detailed proofs, exercises, and solutions.
Format: Hardback
Length: 368 pages
Publication date: 03 September 2021
Publisher: ISTE Ltd
From Euclidian to Hilbert Spaces delves into the profound transition from finite-dimensional Euclidian spaces to infinite-dimensional Hilbert spaces, a concept that may pose challenges for non-specialists to comprehend. The central theme revolves around exploring the similarities and distinctions between the properties of finite and infinite dimensions, emphasizing the critical importance of coherence between algebraic and topological structures. This coherence establishes Hilbert spaces as the infinite-dimensional counterparts that bear the closest resemblance to Euclidian spaces.
This book serves as a comprehensive guide, weaving together various threads to unravel the intricacies of this subject. The Fourier transform assumes a central role, beginning with the discrete Fourier transform (DFT), its applications in signal and image processing, traversing the Fourier series, and culminating in its utilization to solve differential equations. Furthermore, the geometric structure of Hilbert spaces and the noteworthy characteristics of bounded linear operators within these spaces are extensively covered. The theorems are presented with meticulous proofs, accompanied by detailed exercises and solutions, aimed at illustrating the diverse applications of the theoretical outcomes.
By delving into these topics, From Euclidian to Hilbert Spaces offers a comprehensive and accessible exploration of the realm of mathematics, providing insights into the foundations of modern physics and engineering. Whether you are a student, researcher, or enthusiast, this book serves as a valuable resource for deepening your understanding of these complex concepts and their applications.
Weight: 668g
Dimension: 238 x 163 x 25 (mm)
ISBN-13: 9781786306821
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