Spectral Geometry of Partial Differential Operators
1st Edition
Published on 17. February 2020
Book
Hardback
378 pages
978-1-138-36071-6 (ISBN)
Description
The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations.
Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains.
Features:
Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators
Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences
Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods.
Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.
Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains.
Features:
Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators
Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences
Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods.
Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.
More details
Series
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Dimensions
Height: 234 mm
Width: 156 mm
Weight
860 gr
ISBN-13
978-1-138-36071-6 (9781138360716)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Michael Ruzhansky | Makhmud Sadybekov | Durvudkhan Suragan
Spectral Geometry of Partial Differential Operators
E-Book
02/2020
1st Edition
Chapman & Hall/CRC
€0.00
Available for download
Michael Ruzhansky | Makhmud Sadybekov | Durvudkhan Suragan
Spectral Geometry of Partial Differential Operators
E-Book
02/2020
1st Edition
Chapman & Hall/CRC
€0.00
Available for download
Persons
Michael Ruzhansky is a Senior Full Professor of Mathematics at Ghent University, Belgium, and a Professor of Mathematics at the Queen Mary University of London, United Kindgdom. He is currently also an Honorary Professor of Pure Mathematics at Imperial College London, where he has been working in the period 2000-2018. His research is devoted to different topics in the analysis of partial differential equations, harmonic and non-harmonic analysis, spectral theory, microlocal analysis, as well as the operator theory and functional inequalities on groups. His research was recognised by the ISAAC Award 2007, Daiwa Adrian Prize 2010, as well as by the Ferran Sunyer I Balaguer Prizes in 2014 and 2018.
Makhmud Sadybekov is a Kazakhstani mathematician who graduated from the Kazakh State University (Almaty, Kazakhstan) in 1985 and received his doctorate in physical-mathematical sciences in 1993. He is a specialist in the field of Ordinary Differential Equations, Partial Differential Equations, Equations of Mathematical Physics, Functional Analysis, Operators Theory. Currently he is Director General at the Institute of Mathematics and Mathematical Modeling in Almaty, Kazakhstan.
Durvudkhan Suragan an associate professor at Nazarbayev University. He won the Ferran Sunyer i Balaguer Prize in 2018. He has previously worked in spectral geometry, and in the theory of subelliptic inequalities at Imperial College London as a research associate and as a leading researcher in the Institute of Mathematics and Mathematical Modeling.
Makhmud Sadybekov is a Kazakhstani mathematician who graduated from the Kazakh State University (Almaty, Kazakhstan) in 1985 and received his doctorate in physical-mathematical sciences in 1993. He is a specialist in the field of Ordinary Differential Equations, Partial Differential Equations, Equations of Mathematical Physics, Functional Analysis, Operators Theory. Currently he is Director General at the Institute of Mathematics and Mathematical Modeling in Almaty, Kazakhstan.
Durvudkhan Suragan an associate professor at Nazarbayev University. He won the Ferran Sunyer i Balaguer Prize in 2018. He has previously worked in spectral geometry, and in the theory of subelliptic inequalities at Imperial College London as a research associate and as a leading researcher in the Institute of Mathematics and Mathematical Modeling.
Content
1. Function spaces. 2. Foundations of linear operator theory. 3. Elements of the spectral theory of differential operators. 4. Symmetric decreasing rearrangements and applications. 5. Inequalities of spectral geometry.