Spectral Geometry of Partial Differential Operators by Michael Ruzhansky
Spectral Geometry of Partial Differential Operators - Table of Contents
1. Functional Spaces
2. Foundations of the Linear Operator Theory
3. Elements of the Spectral Theory of Differential Operators
4. Symmetric Decreasing Rearrangements and Applications
5. Inequalities of Spectral Geometry
What You Will Learn in Spectral Geometry of Partial Differential Operators
"Spectral Geometry of Partial Differential Operators" by Michael Ruzhansky, Makhmud Sadybekov, and Durvudkhan Suragan is a comprehensive guide to "spectral geometry", "partial differential operators", "operator theory", "eigenvalues", and "mathematical analysis". The book explores how the shape and geometry of domains influence the spectrum of differential operators, focusing on connections between geometric properties and analytical results. It is designed for graduate students, researchers, and mathematicians interested in the interplay between geometry, analysis, and PDEs.
The first part of the book introduces the essential mathematical foundations, including function spaces, linear operators, and basic spectral theory. Readers gain a clear understanding of how self-adjoint and non-self-adjoint operators behave and how their eigenvalues can be studied in various geometric contexts. Each concept is illustrated with examples and rigorous proofs, emphasizing intuition alongside formalism. Key spectral inequalities are derived and analyzed, showing how geometric constraints affect eigenvalue distributions and operator properties.
Later chapters apply these theories to more complex problems, such as spectral estimates for higher-order operators, boundary value problems, and modern techniques in spectral analysis. The book balances theory and application, helping readers connect abstract operator theory with practical spectral problems. By combining clear exposition, detailed proofs, and practical examples, it serves as both a reference and a learning tool for those working in PDEs, spectral theory, and mathematical physics.
Book Details & Specifications
Title:
Spectral Geometry of Partial Differential Operators by Michael Ruzhansky
Publisher:
Chapman and Hall
Year:
2020
Pages:
378
Type:
PDF
Language:
English
ISBN-10 #:
1138360716
ISBN-13 #:
978-1138360716
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Michael Ruzhansky
The author
Michael Ruzhansky
is a distinguished mathematician and professor at Ghent University and Queen Mary University of London, specializing in "partial differential equations", "spectral theory", "harmonic analysis", "operator theory", and "mathematical physics". He has received international recognition, including the ISAAC Award and the Ferran Sunyer i Balaguer Prize, for his contributions to analysis and PDEs. Makhmud Sadybekov and Durvudkhan Suragan are experts in "differential equations", "functional analysis", "operator theory", "spectral geometry", and "PDE research". Sadybekov leads the Institute of Mathematics in Kazakhstan, while Suragan is a professor at Nazarbayev University. Both have contributed significantly to modern spectral theory and mathematical analysis.
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