MARC record from Internet Archive

LEADER: 06636cam 2200817 a 4500
001 ocm28181906
003 OCoLC
005 20200630073013.0
008 930507s1993 gw a b 001 0 eng
010 $a 93014009
040 $aDLC$beng$cDLC$dMUQ$dBAKER$dNLGGC$dBTCTA$dYDXCP$dGBVCP$dZWZ$dGEBAY$dOCLCQ$dOCLCF$dOCLCQ$dOCLCO$dDEBBG$dOCLCQ$dVGM$dOCLCQ$dOCLCO$dCPO$dOCLCQ$dOCLCO$dUKMGB$dHUELT
016 7 $a930960343$2DE-101
016 7 $a006189688$2Uk
020 $a3540568786$q(Berlin ;$qacid-free)
020 $a9783540568780$q(Berlin ;$qacid-free)
020 $a0387568786$q(New York ;$qacid-free)
020 $a9780387568782$q(New York ;$qacid-free)
035 $a(OCoLC)28181906
050 00 $aQA3$b.L28 no. 1549
082 00 $a510 s$a515/.45$220
084 $a31.46$2bcl
084 $a31.45$2bcl
084 $a31.76$2bcl
084 $a*65R20$2msc
084 $a45E10$2msc
084 $a45G05$2msc
084 $a65-02$2msc
084 $aSI 850$2rvk
084 $a27$2sdnb
084 $2msc$a65R20
100 1 $aVaĭnikko, G.
245 10 $aMultidimensional weakly singular integral equations /$cGennadi Vainikko.
260 $aBerlin ;$aNew York :$bSpringer-Verlag,$c©1993.
300 $axi, 158 pages :$billustrations ;$c24 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
338 $avolume$bnc$2rdacarrier
490 1 $aLecture notes in mathematics ;$v1549
504 $aIncludes bibliographical references and index.
505 2 $a1. Some Problems Leading to Multidimensional Weakly Singular Integral Equations -- 1.1. An interior-exterior problem -- 1.2. A physical background (n = 2) -- 1.3. Integral equation formulation [actual symbol not reproducible] -- 1.4. Integral equation formulation (n = 2) -- 1.5. Radiation transfer problem -- 1.6. Integral equation formulation of the radiation transfer problem -- 1.7. Peierls integral equations -- 2. Preliminaries -- 2.1. Metric d[subscript G] and space BC(G*) -- 2.2. Weakly singular integral operators -- 2.3. Compactness of a weakly singular integral operator -- 2.4. Weakly singular integral operators with differentiable kernels -- 2.5. Weighted space [actual symbol not reproducible] -- 2.6. Weighted space [actual symbol not reproducible] -- 3. Smoothness of the Solution -- 3.1. The class of weakly singular kernels -- 3.2. Main results and comments -- 3.3. Differentiation of weakly singular integral -- 3.4. Estimates of the derivatives of Tu -- 3.5. Proof of Theorem 3.1 -- 3.6. Tangential differentiation of weakly singular integral -- 3.7. Estimates of the tangential derivatives of Tu -- 3.8. Proof of Theorem 3.2 -- 3.9. Sharpness of Theorem 3.1 (general analysis) -- 3.10. Sharpness of Theorem 3.1 (analysis of model examples) -- 3.11. Two dimensional integral equation with a logarithmically singular kernel -- 4. Outlines of Discrete Convergence Theory -- 4.1. Discrete convergence and discrete compactness of a family of elements -- 4.2. Example -- 4.3. Discrete convergence of a family of linear operators -- 4.4. Discrete convergence of approximate solutions -- 4.5. Convergence and convergence rates in eigenvalue problems -- 4.6. Approximation of non-linear equations -- 5. Piecewise Constant Collocation and Related Methods -- 5.1. Assumptions about the boundary -- 5.2. Partition of G -- 5.3. PCCM and related methods -- 5.4. Convergence rates of the methods -- 5.5. Block scheme of the proof of Theorem 5.1 -- 5.6. Compact convergence of the discretized operators -- 5.7. Approximation error of the basic method -- 5.8. Estimation of prolonged approximate solution -- 5.9. Proof of assertion (ii) -- 5.10. Proof of assertion (iii) -- 5.11. Proof of assertion (iv) -- 5.12. Two grid iteration method -- 5.13. Initial guesses -- 5.14. Amount of arithmetical work -- 5.15. Eigenvalue problem -- 6. Composite Cubature Algorithms -- 6.1. Partition of G and composite cubature formulae -- 6.2. Basic methods -- 6.3. Refined cubatures for the evaluation of the coefficients -- 6.4. Error analysis (preliminaries) -- 6.5. Error analysis of Algorithms 6.1 and 6.2 -- 6.6. Error estimates for approximate solution -- 6.7. Some further algorithms -- 6.8. Two grid methods -- 6.9. Case of convolution type integral equations -- 7. Higher Order Methods -- 7.1. Space [actual symbol not reproducible] -- 7.2. Piecewise polynomial interpolation -- 7.3. Error estimates of the interpolation -- 7.4. Piecewise polynomial collocation method -- 7.5. Error estimates at the collocation points -- 7.6. Superconvergence at the collocation points -- 7.7. Piecewise constant collocation (m = 1) -- 7.8. Piecewise polylinear collocation (m = 2) -- 7.9. Piecewise polysquare collocation (m = 3) -- 8. Nonlinear Integral Equation -- 8.1. Smoothness of the solution -- 8.2. Piecewise constant collocation and related methods -- 8.3. Higher order methods.
650 0 $aIntegral equations$xAsymptotic theory.
650 6 $aÉquations intégrales$xThéorie asymptotique.
650 7 $aIntegral equations$xAsymptotic theory.$2fast$0(OCoLC)fst00975508
650 17 $aIntegraalvergelijkingen.$2gtt
650 7 $aAsymptotische Methode$2gnd
650 7 $aDiskretisierung$2gnd
650 7 $aIntegralgleichung$2gnd
650 7 $aSchwache Singularität$2gnd
650 7 $aÉquations intégrales$xThéorie asymptotique.$2ram
650 04 $aintegrálegyenletek
653 0 $aIntegral$aAsymptotic theory
776 08 $iOnline version:$aVaĭnikko, G.$tMultidimensional weakly singular integral equations.$dBerlin ; New York : Springer-Verlag, ©1993$w(OCoLC)625890651
830 0 $aLecture notes in mathematics (Springer-Verlag) ;$v1549.
856 41 $3Table of contents$uhttp://www.gbv.de/dms/hbz/toc/ht004951893.pdf
856 41 $3Table of contents$uhttp://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005093366&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
856 42 $3Inhaltstext$uhttp://www.zentralblatt-math.org/zmath/en/search/?an=0789.65097
856 $31850-9999$uhttp://www.springer.com/gb/$xBLDSS
938 $aBaker & Taylor$bBKTY$c37.95$d37.95$i0387568786$n0002325821$sactive
938 $aBaker and Taylor$bBTCP$n93014009
938 $aYBP Library Services$bYANK$n100041423
029 1 $aAU@$b000010110841
029 1 $aDEBBG$bBV007745899
029 1 $aGBVCP$b12600319X
029 1 $aGEBAY$b1876285
029 1 $aNLGGC$b107807378
029 1 $aNZ1$b3629994
029 1 $aYDXCP$b324992
029 1 $aZWZ$b017090547
029 1 $aUKMGB$b006189688
994 $aZ0$bP4A
948 $hNO HOLDINGS IN P4A - 282 OTHER HOLDINGS