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04425nam a22006015i 4500 |
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978-3-7643-8751-8 |
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DE-He213 |
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20210616145625.0 |
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cr nn 008mamaa |
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100301s2008 sz | s |||| 0|eng d |
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|a 9783764387518
|9 978-3-7643-8751-8
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|a 10.1007/978-3-7643-8751-8
|2 doi
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|a QA150-272
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|a PBF
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|a MAT002000
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|a 512
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|a Didenko, Victor.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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|a Approximation of Additive Convolution-Like Operators
|h [electronic resource] :
|b Real C*-Algebra Approach /
|c by Victor Didenko, Bernd Silbermann.
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| 250 |
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|a 1st ed. 2008.
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| 264 |
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|a Basel :
|b Birkhäuser Basel :
|b Imprint: Birkhäuser,
|c 2008.
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| 300 |
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|a XII, 306 p.
|b online resource.
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|a text
|b txt
|2 rdacontent
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|a computer
|b c
|2 rdamedia
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|a online resource
|b cr
|2 rdacarrier
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|a text file
|b PDF
|2 rda
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1 |
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|a Frontiers in Mathematics,
|x 1660-8046
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| 505 |
0 |
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|a Complex 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.
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|a Various 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.
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| 650 |
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|a Algebra.
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| 650 |
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|a Operator theory.
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| 650 |
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|a Numerical analysis.
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| 650 |
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|a Integral equations.
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| 650 |
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|a Integral transforms.
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| 650 |
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|a Operational calculus.
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| 650 |
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|a Partial differential equations.
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| 650 |
1 |
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|a Algebra.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M11000
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| 650 |
2 |
4 |
|a Operator Theory.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12139
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| 650 |
2 |
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|a Numerical Analysis.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M14050
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| 650 |
2 |
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|a Integral Equations.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12090
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| 650 |
2 |
4 |
|a Integral Transforms, Operational Calculus.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12112
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| 650 |
2 |
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|a Partial Differential Equations.
|0 https://scigraph.springernature.com/ontologies/product-market-codes/M12155
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| 700 |
1 |
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|a Silbermann, Bernd.
|e author.
|4 aut
|4 http://id.loc.gov/vocabulary/relators/aut
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| 710 |
2 |
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|a SpringerLink (Online service)
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| 773 |
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|t Springer Nature eBook
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| 776 |
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8 |
|i Printed edition:
|z 9783764398217
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| 776 |
0 |
8 |
|i Printed edition:
|z 9783764387501
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| 830 |
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|a Frontiers in Mathematics,
|x 1660-8046
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| 856 |
4 |
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|u https://doi.org/10.1007/978-3-7643-8751-8
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| 912 |
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|a ZDB-2-SMA
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| 912 |
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|a ZDB-2-SXMS
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| 950 |
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|a Mathematics and Statistics (SpringerNature-11649)
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| 950 |
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|a Mathematics and Statistics (R0) (SpringerNature-43713)
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