LEADER 03903nam 2200673Ia 450 001 9910782101003321 005 20200520144314.0 010 $a3-7643-8751-3 024 7 $a10.1007/978-3-7643-8751-8 035 $a(CKB)1000000000491949 035 $a(EBL)364352 035 $a(OCoLC)288569671 035 $a(SSID)ssj0000517157 035 $a(PQKBManifestationID)11346901 035 $a(PQKBTitleCode)TC0000517157 035 $a(PQKBWorkID)10486860 035 $a(PQKB)10348373 035 $a(SSID)ssj0000492147 035 $a(PQKBManifestationID)11929972 035 $a(PQKBTitleCode)TC0000492147 035 $a(PQKBWorkID)10478456 035 $a(PQKB)10894271 035 $a(DE-He213)978-3-7643-8751-8 035 $a(MiAaPQ)EBC364352 035 $a(Au-PeEL)EBL364352 035 $a(CaPaEBR)ebr10252062 035 $a(PPN)129063347 035 $a(EXLCZ)991000000000491949 100 $a20080325d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aApproximation of additive convolution-like operators$b[electronic resource] $ereal C*-algebra approach /$fVictor D. Didenko, Bernd Silbermann 205 $a1st ed. 2008. 210 $aBasel ;$aBoston $cBirkha?user$dc2008 215 $a1 online resource (315 p.) 225 1 $aFrontiers in mathematics 300 $aDescription based upon print version of record. 311 $a3-7643-8750-5 320 $aIncludes bibliographical references and index. 327 $aComplex and Real Algebras -- Approximation of Additive Integral Operators on Smooth Curves -- Approximation Methods for the Riemann-Hilbert Problem -- Piecewise Smooth and Open Contours -- Approximation Methods for the Muskhelishvili Equation -- Numerical Examples. 330 $aVarious aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated ? and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory. However,invariousapplicationsthereoftenarisecontinuousoperatorsacting on complex Banach spaces that are not linear but only additive ? i. e. , A(x+y)= Ax+Ay for all x,y from a given Banach space. It is easily seen that additive operators 1 are R-linear provided they are continuous. 410 0$aFrontiers in mathematics. 606 $aC*-algebras 606 $aConvolutions (Mathematics) 615 0$aC*-algebras. 615 0$aConvolutions (Mathematics) 676 $a512.55 700 $aDidenko$b Victor D$01473767 701 $aSilbermann$b Bernd$f1941-$060485 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782101003321 996 $aApproximation of additive convolution-like operators$93687076 997 $aUNINA