LEADER 05664nam 2200637 a 450 001 9910463061403321 005 20200520144314.0 010 $a0-88385-970-X 035 $a(CKB)2670000000386409 035 $a(EBL)3330358 035 $a(SSID)ssj0000667044 035 $a(PQKBManifestationID)11379017 035 $a(PQKBTitleCode)TC0000667044 035 $a(PQKBWorkID)10674009 035 $a(PQKB)10582971 035 $a(UkCbUP)CR9780883859704 035 $a(MiAaPQ)EBC3330358 035 $a(Au-PeEL)EBL3330358 035 $a(CaPaEBR)ebr10722469 035 $a(OCoLC)817963747 035 $a(EXLCZ)992670000000386409 100 $a20020129d2002 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aInequalities from complex analysis$b[electronic resource] /$fJohn P. D'Angelo 210 $a[Washington, D.C.] $cMathematical Association of America$dc2002 215 $a1 online resource (280 p.) 225 1 $aThe Carus mathematical monographs ;$vno. 28 300 $aDescription based upon print version of record. 311 $a0-88385-033-8 320 $aIncludes bibliographical references (p. 257-259) and index. 327 $a""Cover ""; ""Title ""; ""Contents""; ""Preface""; ""I. Complex Numbers""; ""I.1 The real number system""; ""I.2 Definition of the complex number field""; ""I.3 Elementary complex geometry""; ""I.4 Alternative definitions of the complex numbers""; ""I.4.1 Using matrices""; ""I.4.2 Using polynomials""; ""I.5 Completeness""; ""I.6 Convergence for power series""; ""I.7 Trigonometry""; ""I.8 Roots of unity""; ""I.9 Summary""; ""II. Complex Euclidean Spaces and Hilbert Spaces""; ""II.1 Hermitian inner products""; ""II.2 Orthogonality, projections and closed subspaces"" 327 $a""II.3 Orthonormal expansion""""II.4 The polarization identity""; ""II.5 Generating functions and orthonormal systems""; ""III. Complex Analysis in Several Variables""; ""III.1 Holomorphic functions""; ""III.2 Some calculus""; ""III.3 The Bergman kernel function""; ""IV. Linear Transformations and Positivity Conditions""; ""IV.1 Adjoints and Hermitian forms""; ""IV.2 Solving linear equations""; ""IV.3 Linearization""; ""IV.4 Eigenvalues and the spectral theorem in finite dimensions""; ""IV.5 Positive definite linear transformations in finite dimensions""; ""IV.6 Hilbert's inequality"" 327 $a""IV.7 Additional inequalities from Fourier analysis""""V. Compact and Integral Operators""; ""V.1 Convergence properties for bounded linear transformations""; ""V.2 Compact operators on Hilbert space""; ""V.3 The spectral theorem for compact Hermitian operators""; ""V.4 Integral operators""; ""V.5 A glimpse at singular integral operators""; ""VI. Positivity Conditions for Real-valued Functions""; ""VI.1 Real variables analogues""; ""VI.2 Real-valued polynomials on C^n""; ""VI.3 Squared norms and quotients of squared norms""; ""VI.4 Plurisubharmonic functions"" 327 $a""VI.5 Positivity conditions for polynomials""""VII. Stabilization and Applications""; ""VII.1 Stabilization for positive bihomogeneous polynomials""; ""VII.2 Positivity everywhere""; ""VII.3 Positivity on the unit sphere""; ""VII.4 Applications to proper holomorphic mappings between balls""; ""VII.5 Positivity on zero sets""; ""VII.6 Proof of stabilization""; ""VIII. Afterword""; ""APPENDIX A""; ""A.1 Algebra""; ""A.2 Analysis""; ""Bibliography""; ""Index"" 330 $aInequalities from Complex Analysis is a careful, friendly exposition of inequalities and positivity conditions for various mathematical objects arising in complex analysis. The author begins by defining the complex number field, and then discusses enough mathematical analysis to reach recently published research on positivity conditions for functions of several complex variables. The development culminates in complete proofs of a stabilization theorem relating two natural positivity conditions for real-valued polynomials of several complex variables. The reader will also encounter the Bergman kernel function, Fourier series, Hermitian linear algebra, the spectral theorem for compact Hermitian operators, plurisubharmonic functions, and some delightful inequalities. Numerous examples, exercises, and discussions of geometric reasoning appear along the way. Undergraduate mathematics majors who have seen elementary real analysis can easily read the first five chapters of this book, and second year graduate students in mathematics can read the entire text. Some physicists and engineers may also find the topics and discussions useful. The inequalities and positivity conditions herein form the foundation for a small but beautiful part of complex analysis. John P. D'Angelo was the 1999 winner of the Bergman Prize; he was cited for several important contributions to complex analysis, including his work on degenerate Levi forms and points of finite type, as well as work, some joint with David Catlin, on positivity conditions in complex analysis 410 0$aCarus mathematical monographs ;$vno. 28. 606 $aFunctions of complex variables 606 $aInequalities (Mathematics) 606 $aMathematical analysis 608 $aElectronic books. 615 0$aFunctions of complex variables. 615 0$aInequalities (Mathematics) 615 0$aMathematical analysis. 676 $a515/.9 700 $aD'Angelo$b John P$060384 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910463061403321 996 $aInequalities from complex analysis$91107681 997 $aUNINA LEADER 00949nam0-22003131i-450 001 990004986260403321 005 20230330121335.0 035 $a000498626 035 $aFED01000498626 035 $a(Aleph)000498626FED01 100 $a19990530g19659999km-y0itay50------ba 101 0 $aeng 102 $aGB 105 $af-------001yy 200 1 $aLettres of Dante Gabriel Rossetti$fedited by Oswald Doughty and John Robert Wahl 210 $aOxford$cThe Clarendon Press$d1965 215 $a2 v. p.$ctav.$d23 cm 327 1 $a1.: 1835-1860$a2.: 1861-1870 700 1$aRossetti,$bDante Gabriel$0132139 702 1$aDoughty,$bOswald 702 1$aWahl,$bJohn Robert 801 0$aIT$bUNINA$gRICA$2UNIMARC 901 $aBK 912 $a990004986260403321 952 $aP 80 (1.1)$bFil. Mod. 23564$fFLFBC 952 $aP 80 (1.2)$bFil. Mod. 23564$fFLFBC 959 $aFLFBC 996 $aLettres of Dante Gabriel Rossetti$93067161 997 $aUNINA LEADER 01042nam a2200277 i 4500 001 991002683509707536 008 150220s2014 enk 001 0 eng d 020 $a9781107076495 035 $ab14216152-39ule_inst 040 $aDip. Studi Giuridici$bita 082 04$a341.42 100 1 $aFitzmaurice, Andrew$0480467 245 10$aSovereignty, property and empire : 1500-2000 $c Andrew Fitzmaurice 260 $aCambridge :$bCambridge University Press,$c2014 300 $a ix, 378 p. ; 24 cm. 440 $aIdeas in context ;$v107 650 4$aDiritto internazionale$xStoria 650 4$aColonizzazione$xStoria 650 4$aPopoli indigeni$xDiritti 650 4$aSovranità$xStoria 907 $a.b14216152$b10-11-17$c20-02-15 912 $a991002683509707536 945 $aLE027 341.42 FIT01.01$g1$i2027000330676$lle027$nProf. Nuzzo$op$pE88.46$q-$rl$s- $t0$u4$v4$w4$x0$y.i15663577$z25-03-15 996 $aSovereignty, property and empire, 1500-2000$9257453 997 $aUNISALENTO 998 $ale027$b20-02-15$cm$da $e-$feng$genk$h0$i0