LEADER 03504nam0 22006013i 450 001 VAN00267519 005 20260910111850.595 017 70$2N$a9781468480382 035 40$a1591458613 100 $a20231122d1968 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aPrincipal Functions$fLeo Sario, Kiyoshi Noshiro$gin collaboration with Mitsuru Nakai 210 $aPrinceton, N.J.$cVan Nostrand$d1968 215 $axviii, 348 p.$cill.$d24 cm 327 $aDuring the decade and a half that has elapsed since the intro­ duction of principal functions (Sario [8 J), they have become impor­ tant tools in an increasing number of branches of modern mathe­ matics. The purpose of the present research monograph is to systematically develop the theory of these functions and their ap­ plications on Riemann surfaces and Riemannian spaces. Apart from brief background information (see below), nothing contained in this monograph has previously appeared in any other book. The basic idea of principal functions is simple: Given a Riemann surface or a Riemannian space R, a neighborhood A of its ideal boundary, and a harmonic function s on A, the principal function problem consists in constructing a harmonic function p on all of R which imitates the behavior of s in A. Here A need not be connected, but may include neighborhoods of isolated points deleted from R. Thus we are dealing with the general problem of constructing harmonic functions with given singularities and a prescribed behavior near the ideal boundary. The function p is called the principal function corresponding to the given A, s, and the mode of imitation of s by p. The significance of principal functions is in their versatility. 410 1$1001VAN00024427$12001 $aˆThe ‰University series in higher mathematics$1210 $aPrinceton$cVan Nostrand 606 $a30-XX$xFunctions of a complex variable [MSC 2020]$3VANC020785$2MF 606 $a32-XX$xSeveral complex variables and analytic spaces [MSC 2020]$3VANC024999$2MF 610 $aConvergence$9KW:K 610 $aDerivatives$9KW:K 610 $aEigenvalue$9KW:K 610 $aExtrema$9KW:K 610 $aFunctions$9KW:K 610 $aHilbert spaces$9KW:K 610 $aHolomorphic Functions$9KW:K 610 $aIntegrals$9KW:K 610 $aIntegrations$9KW:K 610 $aInterpolations$9KW:K 610 $aLogarithms$9KW:K 610 $aMaximum$9KW:K 610 $aMeasures$9KW:K 610 $aOperators$9KW:K 610 $aRiemann surfaces$9KW:K 620 $aUS$dPrinceton$3VANL000078 700 1$aSario$bLeo$3VANV040482$041934 701 1$aNoshiro$bKiyoshi$3VANV207421$056067 702 1$aNakai$bMitsuru$3VANV040483 712 $aVan Nostrand Reinhold $3VANV108090$4650 790 1$aSario, L.$zSario, Leo$3VANV259200 790 1$aNakai, M.$zNakai, Mitsuru$3VANV259201 801 $aIT$bSOL$c20260911$gRICA 856 4 $uhttps://doi.org/10.1007/978-1-4684-8038-2$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00267519 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 7266 $e08eMF7266 20231127 996 $aPrincipal Functions$93596744 997 $aUNICAMPANIA