By Olli Lehto (auth.), Cabiria Andreian Cazacu, Nicu Boboc, Martin Jurchescu, Ion Suciu (eds.)
Read or Download Complex Analysis — Fifth Romanian-Finnish Seminar: Part 1 Proceedings of the Seminar held in Bucharest, June 28 – July 3, 1981 PDF
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Extra info for Complex Analysis — Fifth Romanian-Finnish Seminar: Part 1 Proceedings of the Seminar held in Bucharest, June 28 – July 3, 1981
Caraman (pr~sent~e dans les monographies (1968,4d°anglais~ 1974) et d~ J°Vaisl~la orie d~s transformations (applications) (1971),ia th4- quasi-r~guliAr6s n-dlmension- n611es fur construite par les travaux de Iu°G°Re~etnlak (Sibirsk. 685-691. Solt G u n domaine d~ Rn et K une constante >w l°Une transformatlon f : G ~ R n est dlte K-quasi-r4guli~r& sl elle est continue de classe ACL n et v~rlfie presqu~ partout dans G 1 "in6galit~ If'(x) In <~ K Jf(x) o~ Jf est le jacobien de f. G. Sarvas,la me- sure Lebesgue de Bf et de f (Bf) est nulle et l~ur dimension de Hausdorf~~est _< n.
Des grace au notions et d'humanlsme l'orientation. Esprits cherchalent philosophiques,ils avec passion des faits,ce qu'il y avait de profond et fondamental si que dans les m a t h 4 m a t i q u e s . Dams leur souv6nlr se confond et nous leur apportons nos coeurs le m~me hommage de re-- connais s~nce. e. everywhere in t ~ second, it was possible to define,also (almost everywhere) instead of domain oi" definition D~ and in the infinlte-dimensional case, the concepts of confor mal capecity, module and extremal length and to 24 give the 3 corresponding equivalent definitions of K-qc (see our paper [81).
If instead of F(r),we consider the class FD(r) of admissible functions p~F(r) satisfying also the additional condition that they are continuous and bounded ponding module in D and O in the complement o£ D, then the cortes- is defined as ~Dr = in~ sup p(x) . ii is the norm in B. e, locally Lioschitzian in D, m continuous in D and such that UlF=l,u ICD=O. The conlormal main reason for which we chose the definition proposed by us is that since the confarmal capacity and module of hm 28 are in fac~ p-capecity ant p-module,respectively,with natural to define as conformal capacit~ and module p=n,thsn,it is in the infinite- dimensional spaces again the p-capaci$~ and She p-module ,bu~ this time with p=~ (a more detailed justification is to be found in our paper );and besides all this,it was not possible for us to find more convenient concepts.