524:
352:
519:{\displaystyle \Omega ({\text{ach}}(\omega )).\ \left(\Omega (\omega )=\omega +i\mathbb {R} ^{n}\subset \mathbb {C} ^{n}\ \left(n\geq 2\right),{\text{ach}}(\omega ):=\omega \cup {\text{Int}}\ {\text{ch}}(\omega )\right)}
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The generalized version of this theorem was first proved by Kazlow (1979), also proved by Boivin and
Dwilewicz (1998) under more less complicated hypothese.
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146:
79:
190:
526:. By "Int ch(S)" we will mean the interior taken in the smallest dimensional space which contains "ch(S)".
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609:
Noguchi, Junjiro (2020). "A brief proof of
Bochner's tube theorem and a generalized tube".
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A classic reference is (Theorem 9). See also for other proofs.
18:
Theorem about holomorphic functions of several complex variables
665:"Extension and Approximation of CR Functions on Tube Manifolds"
547:. Princeton mathematical series. Princeton University Press.
187:
can be extended to a function holomorphic on the convex hull
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636:Transactions of the American Mathematical Society
349:can be continuously extended to a CR function on
180:{\displaystyle \Omega =\omega +i\mathbb {R} ^{n}}
703:
580:(12). American Mathematical Society: 4203–4207.
574:Proceedings of the American Mathematical Society
662:
104:{\displaystyle \omega \subset \mathbb {R} ^{n}}
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111:be a connected open set. Then every function
33:) shows that every function holomorphic on a
212:{\displaystyle \operatorname {ch} (\Omega )}
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663:Boivin, André; Dwilewicz, Roman (1998).
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570:"A Proof of Bochner's Tube Theorem"
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543:Bochner, S.; Martin, W.T. (1948).
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649:10.1090/S0002-9947-1979-0542875-5
632:"CR functions and tube manifolds"
342:{\displaystyle \Omega (\omega )}
278:{\displaystyle \mathbb {R} ^{n}}
59:{\displaystyle \mathbb {C} ^{n}}
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587:10.1090/S0002-9939-09-10057-6
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717:Theorems in complex analysis
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712:Several complex variables
545:Several Complex Variables
316:. Then every continuous
249:{\displaystyle \omega }
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309:{\displaystyle C^{2}}
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133:{\displaystyle f(z)}
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630:Kazlow, M. (1979).
568:Hounie, J. (2009).
320:on the tube domain
140:holomorphic on the
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31:Salomon Bochner
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318:CR function
142:tube domain
68:convex hull
35:tube domain
29:(named for
23:mathematics
706:Categories
616:2007.04597
530:References
506:ω
487:∪
484:ω
475:ω
453:≥
427:⊂
406:ω
397:ω
391:Ω
371:ω
357:Ω
334:ω
328:Ω
244:ω
204:Ω
198:
157:ω
151:Ω
87:⊂
84:ω
596:40590656
642:: 153.
234:Theorem
74:Theorem
691:117646
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383:
687:JSTOR
611:arXiv
592:JSTOR
287:class
549:ISBN
236:Let
76:Let
677:doi
673:350
644:doi
640:255
582:doi
578:137
491:Int
468:ach
364:ach
285:of
37:in
21:In
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499:ch
481::=
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