| 000 | 05004nam a22005895i 4500 | ||
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| 001 | 978-3-031-65133-5 | ||
| 003 | DE-He213 | ||
| 005 | 20251030113126.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 241004s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031651335 _9978-3-031-65133-5 |
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| 024 | 7 |
_a10.1007/978-3-031-65133-5 _2doi |
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| 050 | 4 | _aQA404.7-405 | |
| 072 | 7 |
_aPBK _2bicssc |
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| 072 | 7 |
_aMAT033000 _2bisacsh |
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| 072 | 7 |
_aPBK _2thema |
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| 100 | 1 |
_aSaff, Edward B. _eauthor. _0(orcid)0000-0003-1079-9074 _1https://orcid.org/0000-0003-1079-9074 _4aut _4http://id.loc.gov/vocabulary/relators/aut _985601 |
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| 245 | 1 | 0 |
_aLogarithmic Potentials with External Fields _h[electronic resource] / _cby Edward B. Saff, Vilmos Totik. |
| 250 | _a2nd ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2024. |
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| 300 |
_aXVI, 594 p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x2196-9701 ; _v316 |
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| 505 | 0 | _aPart 1 Fundamentals. I Weighted Potentials -- II Recovery of Measures, Green Functions and Balayage -- III Weighted Polynomials -- IV Determination of the Extremal Measure -- Part 2 Applications and Generalizations -- V Extremal Point Methods -- VI Weights on the Real Line -- VII Applications Concerning Orthogonal Polynomials -- VIII Signed Measures -- IX Some Problems from Physics -- X Generalizations -- Part 3 Appendices -- A.I Basic Tools -- A.II The Dirichlet Problem and Harmonic Measures -- A.III Weighted approximation in ℂᴺ -- A.IV Classical Logarithmic Potential Theory. | |
| 520 | _aThis is the second edition of an influential monograph on logarithmic potentials with external fields, incorporating some of the numerous advancements made since the initial publication. As the title implies, the book expands the classical theory of logarithmic potentials to encompass scenarios involving an external field. This external field manifests as a weight function in problems dealing with energy minimization and its associated equilibria. These weighted energies arise in diverse applications such as the study of electrostatics problems, orthogonal polynomials, approximation by polynomials and rational functions, as well as tools for analyzing the asymptotic behavior of eigenvalues for random matrices, all of which are explored in the book. The theory delves into diverse properties of the extremal measure and its logarithmic potentials, paving the way for various numerical methods. This new, updated edition has been thoroughly revised and is reorganized into three parts, Fundamentals, Applications and Generalizations, followed by the Appendices. Additions to the new edition include: new material on the following topics: analytic and C² weights, differential and integral formulae for equilibrium measures, constrained energy problems, vector equilibrium problems, and a probabilistic approach to balayage and harmonic measures; a new chapter entitled Classical Logarithmic Potential Theory, which conveniently summarizes the main results for logarithmic potentials without external fields; several new proofs and sharpened forms of some main theorems; expanded bibliographic and historical notes with dozens of additional references. Aimed at researchers and students studying extremal problems and their applications, particularly those arising from minimizing specific integrals in the presence of an external field, this book assumes a firm grasp of fundamental real and complex analysis. It meticulously develops classical logarithmic potential theory alongside the more comprehensive weighted theory. | ||
| 650 | 0 |
_aPotential theory (Mathematics). _972223 |
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| 650 | 0 |
_aApproximation theory. _974825 |
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| 650 | 0 | _aFourier analysis. | |
| 650 | 0 |
_aFunctions of complex variables. _972222 |
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| 650 | 0 | _aNumerical analysis. | |
| 650 | 1 | 4 |
_aPotential Theory. _972226 |
| 650 | 2 | 4 |
_aApproximations and Expansions. _974827 |
| 650 | 2 | 4 | _aFourier Analysis. |
| 650 | 2 | 4 |
_aFunctions of a Complex Variable. _972224 |
| 650 | 2 | 4 | _aNumerical Analysis. |
| 700 | 1 |
_aTotik, Vilmos. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _985602 |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031651328 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031651342 |
| 830 | 0 |
_aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, _x2196-9701 ; _v316 _980074 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-65133-5 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 999 |
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