000 | 04032nam a22005415i 4500 | ||
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001 | 978-3-540-46949-0 | ||
003 | DE-He213 | ||
005 | 20190213151452.0 | ||
007 | cr nn 008mamaa | ||
008 | 121227s1991 gw | s |||| 0|eng d | ||
020 |
_a9783540469490 _9978-3-540-46949-0 |
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024 | 7 |
_a10.1007/BFb0084665 _2doi |
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050 | 4 | _aQA431 | |
072 | 7 |
_aPBKL _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBKL _2thema |
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082 | 0 | 4 |
_a515.45 _223 |
100 | 1 |
_aGorenflo, Rudolf. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
245 | 1 | 0 |
_aAbel Integral Equations _h[electronic resource] : _bAnalysis and Applications / _cby Rudolf Gorenflo, Sergio Vessella. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg : _bImprint: Springer, _c1991. |
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300 |
_aX, 222 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 |
||
490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1461 |
|
505 | 0 | _aBasic theory and representation formulas -- Applications of Abel's original integral equation: Determination of potentials -- Applications of a transformed abel integral equation -- Smoothing properties of the abel operators -- Existence and uniqueness theorems -- Relations between abel transform and other integral transforms -- Nonlinear abel integral equations of second kind -- Illposedness and stabilization of linear abel integral equations of first kind -- On numerical treatment of first kind abel integral equations. | |
520 | _aIn many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications. | ||
650 | 0 | _aIntegral equations. | |
650 | 0 | _aGlobal analysis (Mathematics). | |
650 | 0 | _aNumerical analysis. | |
650 | 1 | 4 |
_aIntegral Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12090 |
650 | 2 | 4 |
_aMathematical Modeling and Industrial Mathematics. _0http://scigraph.springernature.com/things/product-market-codes/M14068 |
650 | 2 | 4 |
_aTheoretical, Mathematical and Computational Physics. _0http://scigraph.springernature.com/things/product-market-codes/P19005 |
650 | 2 | 4 |
_aAnalysis. _0http://scigraph.springernature.com/things/product-market-codes/M12007 |
650 | 2 | 4 |
_aNumerical Analysis. _0http://scigraph.springernature.com/things/product-market-codes/M14050 |
700 | 1 |
_aVessella, Sergio. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783662201886 |
776 | 0 | 8 |
_iPrinted edition: _z9783540536680 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1461 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/BFb0084665 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
912 | _aZDB-2-BAE | ||
999 |
_c10784 _d10784 |