000 03388nam a22004935i 4500
001 978-3-540-46949-0
003 DE-He213
005 20160624101825.0
007 cr nn 008mamaa
008 121227s1991 gw | s |||| 0|eng d
020 _a9783540469490
_9978-3-540-46949-0
024 7 _a10.1007/BFb0084665
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515
_223
100 1 _aGorenflo, Rudolf.
_eauthor.
245 1 0 _aAbel Integral Equations
_h[electronic resource] :
_bAnalysis and Applications /
_cby Rudolf Gorenflo, Sergio Vessella.
260 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c1991.
300 _aX, 222 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
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 _aMathematics.
650 0 _aGlobal analysis (Mathematics).
650 0 _aNumerical analysis.
650 1 4 _aMathematics.
650 2 4 _aAnalysis.
650 2 4 _aNumerical Analysis.
700 1 _aVessella, Sergio.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540536680
786 _dSpringer
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1461
856 4 0 _uhttp://dx.doi.org/10.1007/BFb0084665
942 _2EBK1488
_cEBK
999 _c30782
_d30782