Spectral Geometry of Partial Differential Operators
Proposal review
Author(s)
Ruzhansky, Michael
Sadybekov, Makhmud
Suragan, Durvudkhan
Language
EnglishAbstract
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.
Keywords
Hardy Littlewood Inequality; Lebesgue integral; Vlasov Poisson Equations; bounded linear operators; Vlasov Poisson System; Fredholm operators; Generalised Derivative; Riesz' inequality; Nonnegative Measurable Functions; spectral geometry; Symmetric Rearrangement; Dirichlet Laplacian; Euler Poisson System; partial differential operators; spectral invariants; linear differential operators; Banach Space; Separable Infinite Dimensional Hilbert Space; Linear Normed Space; Cauchy Sequence; Hilbert Space; Linear SpaceDOI
10.1201/9780429432965ISBN
9780429780578, 9780429780554, 9780429432965, 9780429780561, 9781138360716, 9780429780578OCN
1140387367Publisher
Taylor & FrancisPublisher website
https://taylorandfrancis.com/Publication date and place
2020Imprint
Chapman and Hall/CRCSeries
Chapman & Hall/CRC Monographs and Research Notes in Mathematics,Classification
Functional analysis and transforms
Mathematical physics
Probability and statistics
Differential calculus and equations
Applied mathematics