Spectral Geometry of Partial Differential Operators
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...
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| פורמט: | Online |
| שפה: | אנגלית |
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Taylor & Francis
2025
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| גישה מקוונת: | ONIX_20250512_9780429780578_54 |
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| _version_ | 1869521282754674688 |
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| author | Ruzhansky, Michael Sadybekov, Makhmud Suragan, Durvudkhan |
| author_browse | Ruzhansky, Michael Sadybekov, Makhmud Suragan, Durvudkhan |
| author_facet | Ruzhansky, Michael Sadybekov, Makhmud Suragan, Durvudkhan |
| author_sort | Ruzhansky, Michael |
| collection | Directory of Open Access Books |
| 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. |
| format | Online |
| id | doab-20.500.12854ir-159253 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Taylor & Francis |
| publisherStr | Taylor & Francis |
| record_format | ojs |
| spelling | doab-20.500.12854ir-1592532025-05-16T05:34:57Z Spectral Geometry of Partial Differential Operators Ruzhansky, Michael Sadybekov, Makhmud Suragan, Durvudkhan 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKF Functional analysis and transforms thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics 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. 2025-05-13T04:10:29Z 2025-05-13T04:10:29Z 2025-05-12T09:35:42Z 2020 book ONIX_20250512_9780429780578_54 https://library.oapen.org/handle/20.500.12657/101514 9780429780578 9780429780554 9780429432965 9780429780561 9781138360716 https://directory.doabooks.org/handle/20.500.12854/159253 eng Chapman & Hall/CRC Monographs and Research Notes in Mathematics open access image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://library.oapen.org/bitstream/20.500.12657/101514/1/9780429780578.pdf Taylor & Francis Chapman and Hall/CRC 10.1201/9780429432965 10.1201/9780429432965 fa69b019-f4ee-4979-8d42-c6b6c476b5f0 9780429780578 9780429780554 9780429432965 9780429780561 9781138360716 Chapman and Hall/CRC 378 open access |
| spellingShingle | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKF Functional analysis and transforms thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics Ruzhansky, Michael Sadybekov, Makhmud Suragan, Durvudkhan Spectral Geometry of Partial Differential Operators |
| title | Spectral Geometry of Partial Differential Operators |
| title_full | Spectral Geometry of Partial Differential Operators |
| title_fullStr | Spectral Geometry of Partial Differential Operators |
| title_full_unstemmed | Spectral Geometry of Partial Differential Operators |
| title_short | Spectral Geometry of Partial Differential Operators |
| title_sort | spectral geometry of partial differential operators |
| topic | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKF Functional analysis and transforms thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics |
| topic_facet | 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 thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKF Functional analysis and transforms thema EDItEUR::P Mathematics and Science::PH Physics::PHU Mathematical physics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBT Probability and statistics thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations thema EDItEUR::P Mathematics and Science::PB Mathematics::PBW Applied mathematics |
| url | ONIX_20250512_9780429780578_54 |
| work_keys_str_mv | AT ruzhanskymichael spectralgeometryofpartialdifferentialoperators AT sadybekovmakhmud spectralgeometryofpartialdifferentialoperators AT suragandurvudkhan spectralgeometryofpartialdifferentialoperators |