LEADER 03168nam 2200481 450 001 9910271006103321 005 20220330193744.0 010 $a1-119-42664-2 010 $a1-119-42651-0 010 $a1-119-42653-7 035 $a(CKB)3710000001403852 035 $a(MiAaPQ)EBC4875241 035 $a(Au-PeEL)EBL4875241 035 $a(CaPaEBR)ebr11395818 035 $a(OCoLC)990550001 035 $a(PPN)253501415 035 $a(EXLCZ)993710000001403852 100 $a20170707h20172017 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 10$aBanach, Frechet, Hilbert and Neumann spaces$hvolume 1 /$fJacques Simon 210 1$aLondon, England ;$aHoboken, New Jersey :$cISTE :$cWiley,$d2017. 210 4$dİ2017 215 $a1 online resource (367 pages) $cillustrations 225 0 $aAnalysis for PDEs Set 311 $a1-78630-009-5 320 $aIncludes bibliographical references and index. 327 $tIntroduction --$tFamiliarization with semi-normed spaces --$tNotations --$tPrerequisites --$gPart 1.$tSemi-normed spaces ;$tSemi-normed spaces --$tComparison of semi-normed spaces --$tBanach, Fre?chet and Neumann spaces --$tHilbert spaces --$tProduct, intersection, sum and quotient of spaces --$gPart 2.$tContinuous mappings ;$tContinuous mappings --$tImages of sets under continuous mappings --$tProperties of mappings in metrizable spaces --$tExtension of mappings, equicontinuity --$tCompactness in mapping spaces --$tSpaces of linear or multilinear mappings --$gPart 3.$tWeak topologies ;$tDuality --$tDual of a subspace --$tWeak topology --$tProperties of sets for the weak topology --$tReflexivity --$tExtractable spaces --$gPart 4.$tDifferential calculus ;$tDifferentiable mappings --$tDifferentiation of multivariable mappings --$tSuccessive differentiations --$tDerivation of functions of one real variable. 330 $aThis book is the first of a set dedicated to the mathematical tools used in partial differential equations derived from physics. Its focus is on normed or semi-normed vector spaces, including the spaces of Banach, Fre?chet and Hilbert, with new developments on Neumann spaces, but also on extractable spaces. The author presents the main properties of these spaces, which are useful for the construction of Lebesgue and Sobolev distributions with real or vector values and for solving partial differential equations. Differential calculus is also extended to semi-normed spaces. Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students - doctoral students, postgraduate students - engineers and researchers without restricting or generalizing the results.--$cSource other than the Library of Congress. 606 $aBanach spaces 615 0$aBanach spaces. 676 $a515.732 700 $aSimon$b Jacques$0342532 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910271006103321 996 $aBanach, Frechet, Hilbert and Neumann spaces$91896924 997 $aUNINA