LEADER 04086oam 2200541 450 001 9910790428703321 005 20190911112729.0 010 $a981-4458-77-5 035 $a(OCoLC)860388264 035 $a(MiFhGG)GVRL8RDO 035 $a(EXLCZ)992550000001114719 100 $a20140402h20132013 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aBochner-Riesz means on Euclidean spaces /$fShanzhen Lu, Beijing Normal University, China, Dunyan Yan, University of Chinese Academy of Sciences, China 210 1$aNew Jersey :$cWorld Scientific,$d[2013] 210 4$d?2013 215 $a1 online resource (viii, 376 pages) $cillustrations 225 0 $aGale eBooks 300 $aDescription based upon print version of record. 311 $a981-4458-76-7 311 $a1-299-83340-3 320 $aIncludes bibliographical references and index. 327 $aContents; Preface; 1 An introduction to multiple Fourier series; 1.1 Basic properties of multiple Fourier series; 1.2 Poisson summation formula; 1.3 Convergence and the opposite results; 1.4 Linear summation; 2 Bochner-Riesz means of multiple Fourier integral; 2.1 Localization principle and classic results on fixed-point convergence; 2.2 Lp-convergence; 2.3 Some basic facts on multipliers; 2.4 The disc conjecture and Fefferman theorem; 2.5 The Lp-boundedness of Bochner-Riesz operator T? with ? > 0; 2.6 Oscillatory integral and proof of Carleson-Sjolin theorem; 2.6.1 Oscillatory integrals 327 $a2.6.2 Proof of Carleson-Sjolin theorem2.7 Kakeya maximal function; 2.8 The restriction theorem of the Fourier transform; 2.9 The case of radial functions; 2.10 Almost everywhere convergence; 2.11 Commutator of Bochner-Riesz operator; 3 Bochner-Riesz means of multiple Fourier series; 3.1 The case of being over the critical index; 3.1.1 Bochner formula; 3.1.2 The localization theorem; 3.1.3 The maximal operator S?*; 3.2 The case of the critical index (general discussion); 3.2.1 Localization problems; 3.2.2 An example of being divergent almost everywhere 327 $a3.9 The saturation problem of the uniform approximation3.10 Strong summation; 4 The conjugate Fourier integral and series; 4.1 The conjugate integral and the estimate of the kernel; 4.2 Convergence of Bochner-Riesz means for conjugate Fourier integral; 4.3 The conjugate Fourier series; 4.4 Kernel of Bochner-Riesz means of conjugate Fourier series; 4.5 The maximal operator of the conjugate partial sum; 4.6 The relations between the conjugate series and integral; 4.7 Convergence of Bochner-Riesz means of conjugate Fourier series; 4.8 (C,1) means in the conjugate case 327 $a4.9 The strong summation of the conjugate Fourier series4.10 Approximation of continuous functions; Bibliography; Index 330 $aThis book mainly deals with the Bochner-Riesz means of multiple Fourier integral and series on Euclidean spaces. It aims to give a systematical introduction to the fundamental theories of the Bochner-Riesz means and important achievements attained in the last 50 years. For the Bochner-Riesz means of multiple Fourier integral, it includes the Fefferman theorem which negates the Disc multiplier conjecture, the famous Carleson-Sjo?lin theorem, and Carbery-Rubio de Francia-Vega's work on almost everywhere convergence of the Bochner-Riesz means below the critical index. For the Bochner-Riesz means o 606 $aFourier series 606 $aEuclidean algorithm 606 $aFourier series$xMathematical models 606 $aEuclidean algorithm$xMathematical models 615 0$aFourier series. 615 0$aEuclidean algorithm. 615 0$aFourier series$xMathematical models. 615 0$aEuclidean algorithm$xMathematical models. 676 $a515.2433 700 $aLu$b Shanzhen$f1939-$0629792 702 $aYan$b Dunyan 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910790428703321 996 $aBochner-Riesz means on Euclidean spaces$93871844 997 $aUNINA LEADER 02047nam 2200349z- 450 001 9910582201003321 005 20220709 010 $a3-7983-3253-3 035 $a(CKB)5700000000101233 035 $a(oapen)https://directory.doabooks.org/handle/20.500.12854/87653 035 $a(oapen)87653 035 $a(EXLCZ)995700000000101233 100 $a20202207d2022 |y 0 101 0 $aeng 135 $aurmn|---annan 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMatching minors in bipartite graphs 210 $aBerlin$cUniversitätsverlag der Technischen Universität Berlin$d2022 215 $a1 electronic resource (476 p.) 225 1 $aFoundations of computing 311 08$a3-7983-3252-5 330 $aIn this thesis we adapt fundamental parts of the Graph Minors series of Robertson and Seymour for the study of matching minors and investigate a connection to the study of directed graphs. We develope matching theoretic to established results of graph minor theory: We characterise the existence of a cross over a conformal cycle by means of a topological property. Furthermore, we develope a theory for perfect matching width, a width parameter for graphs with perfect matchings introduced by Norin. here we show that the disjoint alternating paths problem can be solved in polynomial time on graphs of bounded width. Moreover, we show that every bipartite graph with high perfect matching width must contain a large grid as a matching minor. Finally, we prove an analogue of the we known Flat Wall theorem and provide a qualitative description of all bipartite graphs which exclude a fixed matching minor. 606 $aAlgorithms & data structures$2bicssc 610 $amatching minor; structural graph theory; bipartite; perfect matching 615 7$aAlgorithms & data structures 700 $aWiederrecht$b Sebastian$4auth$01293616 906 $aBOOK 912 $a9910582201003321 996 $aMatching minors in bipartite graphs$93022664 997 $aUNINA