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010   $a3-319-20140-9
024 7 $a10.1007/978-3-319-20140-5
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035   $a(EBL)3568054
035   $a(SSID)ssj0001546753
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035   $a(PQKBTitleCode)TC0001546753
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035   $a(DE-He213)978-3-319-20140-5
035   $a(MiAaPQ)EBC3568054
035   $a(PPN)188457437
035   $a(EXLCZ)993710000000460479
100   $a20150805d2015      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aFundamental solutions of linear partial differential operators $etheory and practice /$fby Norbert Ortner, Peter Wagner
205   $a1st ed. 2015.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015.
215   $a1 online resource (407 p.)
300   $aDescription based upon print version of record.
311 08$a3-319-20139-5 
320   $aIncludes bibliographical references and index.
327   $aIntroduction -- I. Distributions and Fundamental Solutions -- II. General Principles for Fundamental Solutions -- III. Parameter Integration -- IV. Quasihyperbolic Systems -- V. Fundamental Matrices of Homogeneous Systems -- Appendix: Table of Operators/Systems with References to Fundamental Solutions/Matrices -- References -- Index.
330   $aThis monograph provides the theoretical foundations needed for the construction of fundamental solutions and fundamental matrices of (systems of) linear partial differential equations. Many illustrative examples also show techniques for finding such solutions in terms of integrals. Particular attention is given to developing the fundamentals of distribution theory, accompanied by calculations of fundamental solutions. The main part of the book deals with existence theorems and uniqueness criteria, the method of parameter integration, the investigation of quasihyperbolic systems by means of Fourier and Laplace transforms, and the representation of fundamental solutions of homogeneous elliptic operators with the help of Abelian integrals. In addition to rigorous distributional derivations and verifications of fundamental solutions, the book also shows how to construct fundamental solutions (matrices) of many physically relevant operators (systems), in elasticity, thermoelasticity, hexagonal/cubic elastodynamics, for Maxwell?s system and others. The book mainly addresses researchers and lecturers who work with partial differential equations. However, it also offers a valuable resource for students with a solid background in vector calculus, complex analysis and functional analysis.
606   $aDifferential equations, Partial
606   $aIntegral transforms
606   $aCalculus, Operational
606   $aFunctional analysis
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aIntegral Transforms, Operational Calculus$3https://scigraph.springernature.com/ontologies/product-market-codes/M12112
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aDifferential equations, Partial.
615  0$aIntegral transforms.
615  0$aCalculus, Operational.
615  0$aFunctional analysis.
615 14$aPartial Differential Equations.
615 24$aIntegral Transforms, Operational Calculus.
615 24$aFunctional Analysis.
676   $a510
700   $aOrtner$b Norbert$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755616
702   $aWagner$b Peter$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910299773803321
996   $aFundamental Solutions of Linear Partial Differential Operators$92546583
997   $aUNINA