484:
196:
479:{\displaystyle \omega (\zeta ,z)={\frac {(n-1)!}{(2\pi i)^{n}}}{\frac {1}{|z-\zeta |^{2n}}}\sum _{1\leq j\leq n}({\overline {\zeta }}_{j}-{\overline {z}}_{j})\,d{\overline {\zeta }}_{1}\land d\zeta _{1}\land \cdots \land d\zeta _{j}\land \cdots \land d{\overline {\zeta }}_{n}\land d\zeta _{n}}
698:
790:
567:
1229:
Martinelli, Enzo (1938), "Alcuni teoremi integrali per le funzioni analitiche di più variabili complesse" [Some integral theorems for analytic functions of several complex variables],
1231:
75:
graduate course in Winter 1940/1941 and were subsequently incorporated, in a
Princeton doctorate thesis (June 1941) by Donald C. May, entitled: An integral formula for analytic functions of
158:
1128:
540:
1265:
100:
footnote 1, that he might have been familiar with the general shape of the formula before
Martinelli, was wholly unjustified and is hereby being retracted.
827:), which actually contains Martinelli's proof of the formula. However, the earlier article is explicitly cited in the later one, as it can be seen from (
1346:
715:
693:{\displaystyle \displaystyle f(z)=\int _{\partial D}f(\zeta )\omega (\zeta ,z)-\int _{D}{\overline {\partial }}f(\zeta )\land \omega (\zeta ,z).}
1426:
1222:
1195:
1150:
1098:
1046:
1431:
1270:
973:
884:
1355:], Contributi del Centro Linceo Interdisciplinare di Scienze Matematiche e Loro Applicazioni (in Italian), vol. 67, Rome:
1156:
1348:
Introduzione elementare alla teoria delle funzioni di variabili complesse con particolare riguardo alle rappresentazioni integrali
1003:
1372:
1356:
1387:[Some reflections on the integral representation of maximal dimension for functions of several complex variables],
1353:
Elementary introduction to the theory of functions of complex variables with particular regard to integral representations
1334:
1013:
876:
1385:"Qualche riflessione sulla rappresentazione integrale di massima dimensione per le funzioni di più variabili complesse"
1142:
1008:
1338:
1257:
36:
801:
1326:
1360:
1030:
32:
1389:
Atti della
Accademia Nazionale dei Lincei. Rendiconti. Classe di Scienze Fisiche, Matematiche e Naturali
1165:
1124:
1072:
915:
862:
1311:
134:
1082:
872:
72:
1232:
Atti della Reale
Accademia d'Italia. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali
17:
858:
64:
Formula (53) of the present paper and a proof of theorem 5 based on it have just been published by
523:
71:. The present author may be permitted to state that these results have been presented by him in a
1295:
940:
1384:
1218:
1191:
1146:
1094:
1042:
932:
880:
1404:
1303:
1279:
1248:
1240:
1209:
1183:
1112:
1086:
1060:
1034:
1020:
990:
956:
924:
898:
1400:
1291:
1205:
1108:
1056:
986:
952:
894:
1408:
1396:
1330:
1307:
1287:
1252:
1244:
1213:
1201:
1179:
1116:
1104:
1064:
1052:
994:
982:
968:
960:
948:
910:
902:
890:
65:
48:
40:
1420:
1299:
1024:
1412:. In this article, Martinelli gives another form to the Martinelli–Bochner formula.
1135:
Integral representations and their application in multidimensional complex analysis
1169:
1076:
866:
1138:
785:{\displaystyle \displaystyle f(z)=\int _{\partial D}f(\zeta )\omega (\zeta ,z).}
1187:
1090:
936:
913:(1943), "Analytic and meromorphic continuation by means of Green's formula",
1175:
1171:
Multidimensional integral representations. Problems of analytic continuation
1130:Интегральные представления и их приложения в многомерном комплексном анализе
868:
1283:
1038:
944:
514:
is a continuously differentiable function on the closure of a domain
1323:
928:
1266:"Sopra una dimostrazione di R. Fueter per un teorema di Hartogs"
1268:[On a proof of R. Fueter of a theorem of Hartogs],
1375:, held by Martinelli during his stay at the Accademia as "
871:, Translations of Mathematical Monographs, vol. 58,
719:
718:
571:
570:
549:. Then the Bochner–Martinelli formula states that if
526:
199:
137:
1078:
The
Bochner-Martinelli integral and its applications
823:), apparently being not aware of the earlier one (
784:
692:
534:
478:
152:
828:
820:
94:
62:
974:The Journal of the Indian Mathematical Society
1029:(reprint of 2nd ed.), Providence, R.I.:
709:is holomorphic the second term vanishes, so
8:
1371:. The notes form a course, published by the
1333:. In this paper Martinelli gives a proof of
1026:Function theory of several complex variables
1004:"Bochner–Martinelli representation formula"
824:
819:Bochner refers explicitly to the article (
44:
739:
717:
643:
637:
591:
569:
528:
527:
525:
470:
454:
444:
425:
403:
387:
377:
372:
363:
353:
343:
333:
311:
295:
290:
275:
269:
260:
221:
198:
144:
140:
139:
136:
971:(1947), "On compact complex manifolds",
1256:. The first paper where the now called
841:
812:
106:
87:
52:
7:
18:Bochner–Martinelli–Koppelman formula
740:
645:
592:
25:
1359:, pp. 236+II, archived from
1271:Commentarii Mathematici Helvetici
81:variables with some applications.
840:Bochner refers to his claim in (
153:{\displaystyle \mathbb {C} ^{n}}
1168:; Myslivets, Simona G. (2015),
1127:; Myslivets, Simona G. (2010),
542:with piecewise smooth boundary
96:However this author's claim in
1373:Accademia Nazionale dei Lincei
1357:Accademia Nazionale dei Lincei
1264:Martinelli, Enzo (1942–1943),
775:
763:
757:
751:
729:
723:
683:
671:
662:
656:
627:
615:
609:
603:
581:
575:
369:
329:
291:
276:
257:
244:
236:
224:
215:
203:
160:the Bochner–Martinelli kernel
1:
877:American Mathematical Society
1427:Theorems in complex analysis
1391:, Series VIII (in Italian),
648:
535:{\displaystyle \mathbb {C} }
449:
382:
358:
338:
1174:, Cham–Heidelberg–New York–
1009:Encyclopedia of Mathematics
31:is a generalization of the
1448:
1383:Martinelli, Enzo (1984b),
1339:Bochner-Martinelli formula
1335:Hartogs' extension theorem
1258:Bochner-Martinelli formula
172:is a differential form in
29:Bochner–Martinelli formula
1432:Several complex variables
1345:Martinelli, Enzo (1984),
1260:is introduced and proved.
1188:10.1007/978-3-319-21659-1
1091:10.1007/978-3-0348-9094-6
115:Bochner–Martinelli kernel
37:several complex variables
33:Cauchy integral formula
1166:Kytmanov, Alexander M.
1125:Kytmanov, Alexander M.
1073:Kytmanov, Alexander M.
1031:AMS Chelsea Publishing
1002:Chirka, E.M. (2001) ,
844:, p. 652, footnote 1).
831:, p. 340, footnote 2).
786:
694:
536:
480:
154:
112:
93:
90:, p. 652, footnote 1).
1182:, pp. xiii+225,
916:Annals of Mathematics
787:
695:
537:
481:
155:
109:, p. 15, footnote *).
1085:, pp. xii+305,
1033:, pp. xvi+564,
829:Martinelli 1942–1943
821:Martinelli 1942–1943
802:Bergman–Weil formula
716:
568:
524:
197:
135:
27:In mathematics, the
1322:. Available at the
49:Salomon Bochner
41:Enzo Martinelli
1329:2012-11-10 at the
1284:10.1007/bf02565649
879:, pp. x+283,
782:
781:
690:
689:
532:
476:
328:
150:
105:Salomon Bochner, (
86:Salomon Bochner, (
1377:Professore Linceo
1223:978-3-319-21659-1
1197:978-3-319-21658-4
1152:978-5-7638-1990-8
1100:978-3-7643-5240-0
1083:Birkhäuser Verlag
1048:978-0-8218-2724-6
1021:Krantz, Steven G.
919:, Second Series,
703:In particular if
651:
555:is in the domain
452:
385:
361:
341:
307:
305:
267:
16:(Redirected from
1439:
1411:
1370:
1369:
1368:
1321:
1320:
1319:
1310:, archived from
1255:
1216:
1160:
1155:, archived from
1119:
1067:
1039:10.1090/chel/340
1016:
997:
969:Bochner, Salomon
963:
911:Bochner, Salomon
905:
859:Aizenberg, L. A.
845:
838:
832:
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498:
489:(where the term
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35:to functions of
21:
1447:
1446:
1442:
1441:
1440:
1438:
1437:
1436:
1417:
1416:
1415:
1382:
1366:
1364:
1344:
1331:Wayback Machine
1317:
1315:
1263:
1228:
1198:
1180:Springer Verlag
1164:
1153:
1145:, p. 389,
1123:
1101:
1071:
1049:
1019:
1001:
967:
929:10.2307/1969103
909:
887:
873:Providence R.I.
863:Yuzhakov, A. P.
857:
853:
848:
839:
835:
825:Martinelli 1938
818:
814:
810:
798:
735:
714:
713:
704:
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566:
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179:
173:
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138:
133:
132:
126:
120:
117:
111:
104:
92:
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66:Enzo Martinelli
61:
23:
22:
15:
12:
11:
5:
1445:
1443:
1435:
1434:
1429:
1419:
1418:
1414:
1413:
1395:(4): 235–242,
1380:
1342:
1278:(1): 340–349,
1274:(in Italian),
1261:
1239:(7): 269–283,
1235:(in Italian),
1226:
1196:
1162:
1151:
1121:
1099:
1069:
1047:
1017:
999:
977:, New Series,
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847:
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833:
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1398:
1394:
1390:
1386:
1381:
1378:
1374:
1363:on 2011-09-27
1362:
1358:
1354:
1350:
1349:
1343:
1340:
1337:by using the
1336:
1332:
1328:
1325:
1314:on 2011-10-02
1313:
1309:
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1301:
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1159:on 2014-03-23
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1361:the original
1352:
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1324:SEALS Portal
1316:, retrieved
1312:the original
1275:
1269:
1236:
1230:
1170:
1157:the original
1134:
1129:
1077:
1025:
1007:
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972:
920:
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867:
842:Bochner 1943
836:
815:
705:
702:
557:
551:
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516:
510:
507:
500:
495:
491:
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185:
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178:of bidegree
174:
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127:
121:
118:
107:Bochner 1947
97:
95:
88:Bochner 1943
77:
68:
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190:defined by
1421:Categories
1409:0599.32002
1367:2011-01-03
1318:2020-07-04
1308:0028.15201
1253:0022.24002
1245:64.0322.04
1214:1341.32001
1139:Красноярск
1117:0834.32001
1065:1087.32001
995:0038.23701
961:0060.24206
903:0537.32002
851:References
1300:119960691
1178:–London:
1176:Dordrecht
1075:(1995) ,
1023:(2001) ,
1014:EMS Press
937:0003-486X
865:(1983) ,
767:ζ
761:ω
755:ζ
741:∂
737:∫
675:ζ
669:ω
666:∧
660:ζ
649:¯
646:∂
635:∫
631:−
619:ζ
613:ω
607:ζ
593:∂
589:∫
468:ζ
461:∧
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447:ζ
438:∧
435:⋯
432:∧
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416:∧
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383:¯
380:ζ
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336:ζ
322:≤
316:≤
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251:π
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201:ω
98:loc. cit.
73:Princeton
1327:Archived
1225:(ebook).
981:: 1–21,
796:See also
103:—
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59:History
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1147:ISBN
1095:ISBN
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933:ISSN
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119:For
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45:1938
1405:Zbl
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1280:doi
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240:!
237:)
234:1
228:n
225:(
219:=
216:)
213:z
210:,
204:(
186:n
184:,
182:n
180:(
175:ζ
170:)
168:z
166:,
164:ζ
146:n
141:C
128:z
122:ζ
78:k
20:)
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