LEADER 03549nam 2200613 450 001 996466587403316 005 20220911000642.0 010 $a3-540-46949-4 024 7 $a10.1007/BFb0084665 035 $a(CKB)1000000000437062 035 $a(SSID)ssj0000320756 035 $a(PQKBManifestationID)12116004 035 $a(PQKBTitleCode)TC0000320756 035 $a(PQKBWorkID)10258149 035 $a(PQKB)10743109 035 $a(DE-He213)978-3-540-46949-0 035 $a(MiAaPQ)EBC5610578 035 $a(Au-PeEL)EBL5610578 035 $a(OCoLC)1078999449 035 $a(MiAaPQ)EBC6842075 035 $a(Au-PeEL)EBL6842075 035 $a(OCoLC)1113040562 035 $a(PPN)155187848 035 $a(EXLCZ)991000000000437062 100 $a20220911d1991 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aAbel integral equations $eanalysis and applications /$fRudolf Gorenflo, Sergio Vessella 205 $a1st ed. 1991. 210 1$aBerlin :$cSpringer-Verlag,$d[1991] 210 4$dİ1991 215 $a1 online resource (X, 222 p.) 225 1 $aLecture notes in mathematics ;$v1461 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-53668-X 320 $aIncludes bibliographical references and index. 327 $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. 330 $aIn many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1461. 606 $aAbel integral equations 615 0$aAbel integral equations. 676 $a515.45 700 $aGorenflo$b Rudolf$042618 702 $aVessella$b Sergio 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996466587403316 996 $aAbel integral equations$9262307 997 $aUNISA