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    Spectral Geometry of Partial Differential Operators

    Proposal review

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    Author(s)
    Ruzhansky, Michael
    Sadybekov, Makhmud
    Suragan, Durvudkhan
    Language
    English
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    Abstract
    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.
    URI
    https://library.oapen.org/handle/20.500.12657/101514
    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 Space
    DOI
    10.1201/9780429432965
    ISBN
    9780429780578, 9780429780554, 9780429432965, 9780429780561, 9781138360716, 9780429780578
    OCN
    1140387367
    Publisher
    Taylor & Francis
    Publisher website
    https://taylorandfrancis.com/
    Publication date and place
    2020
    Imprint
    Chapman and Hall/CRC
    Series
    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
    Pages
    378
    Rights
    https://creativecommons.org/licenses/by-nc-nd/4.0/
    • Imported or submitted locally

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    License

    • If not noted otherwise all contents are available under Attribution 4.0 International (CC BY 4.0)

    Credits

    • logo EU
    • This project received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 683680, 810640, 871069 and 964352.

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