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On the envelope of holomorphy of a generalized tube in C n C n中广义管的全纯包络
Kodai Mathematical Seminar Reports Pub Date : 1963-06-01 DOI: 10.2996/KMJ/1138844758
J. Kajiwara
{"title":"On the envelope of holomorphy of a generalized tube in C n","authors":"J. Kajiwara","doi":"10.2996/KMJ/1138844758","DOIUrl":"https://doi.org/10.2996/KMJ/1138844758","url":null,"abstract":"In 1937 Stein [10] proved that the envelope of holomorphy of a tube-domain in C coincides with its envelope of convexity. We can find no difficulty in extending the above Stein's proof to the case in C. In 1938 Bochner [2] obtained the above Stein's Theorem quite independently in O. Later Hi tot u mat u [7] gave a new and elegant proof and Bremermann [5] extended the above Stein's Theorem in complex Banach spaces. The main purpose of the present paper is to extend the above Stein's Theorem to a generalized tube in C. The main method is based on the Levi's problem and the convergence theorem concerning the domain of holomorphy.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"108 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125221801","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
Some expansion theorems for stochastic processes. II. 随机过程的几个展开式定理。2
Kodai Mathematical Seminar Reports Pub Date : 1963-06-01 DOI: 10.2996/KMJ/1138844783
Hirohisa Hatori
{"title":"Some expansion theorems for stochastic processes. II.","authors":"Hirohisa Hatori","doi":"10.2996/KMJ/1138844783","DOIUrl":"https://doi.org/10.2996/KMJ/1138844783","url":null,"abstract":"which has been treated by Kawata [3] for r=Q and a =1/2 with somewhat different conditions, and extended by the author [1] for r=Q, 1, 2, ••• and 0^<*<1 with the above conditions (i)— (v). In this paper, we shall show (1.1) for X(t)=f(t)+φ(t)8(t), where φ(u) is a numerical valued function. If 0(s)>0, — oo<s<oo, then, for this process X(t the correlation coefficient of X(t) and X(s) is a function of t— s only. In section 2, Taylor expansion of 8(t) is discussed and, in section 3, the expansion theorem for Γ χ(t-—}dH(s) J-oo n / is given, where X(t)=f(t)+φ(f)8(t), -oo<t<oo.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122104667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Dependence properties of solutions on the retardation and initial values in the theory of difference-differential equations 微分方程理论中解对迟滞值和初值的依赖性质
Kodai Mathematical Seminar Reports Pub Date : 1963-06-01 DOI: 10.2996/KMJ/1138844755
S. Sugiyama
{"title":"Dependence properties of solutions on the retardation and initial values in the theory of difference-differential equations","authors":"S. Sugiyama","doi":"10.2996/KMJ/1138844755","DOIUrl":"https://doi.org/10.2996/KMJ/1138844755","url":null,"abstract":"as the retardation h tends to zero, and stated that the same method they used can be applied to demonstrate the corresponding result for more general differentialdifference equations. The author [6] has discussed the same problems as above for general equations (0.1), in which f(ty x, y) is a continuous function denned in a bounded and closed domain and satisfies Lipschitz condition, and he obtained some results as direct consequences of the dependence properties of solutions on the retardation h, as well as the behavior of solutions as h tends to zero. The purpose of this paper is to discuss the problems of dependence properties of solutions of (0.1) on retarded arguments and initial values for the case where t varies in the infinite interval.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"712 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1963-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133817332","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Conformal mapping of polygonal domains 多边形域的保角映射
Kodai Mathematical Seminar Reports Pub Date : 1950-09-01 DOI: 10.2996/KMJ/1138833469
Yūsaku Komatu
{"title":"Conformal mapping of polygonal domains","authors":"Yūsaku Komatu","doi":"10.2996/KMJ/1138833469","DOIUrl":"https://doi.org/10.2996/KMJ/1138833469","url":null,"abstract":"1o In a recent paper an explicit formula has been established for an analytic function mapping an annulus onto a domain which contains the point at infinity in its interior and whose boundary consists of two rectilinear polygons (see Satz 8 in [2]). Since the formula has been obtained there as a corollary of a general representation theorem for analytic functions in which the Villat-Stieltjes formula has been taken into account as an essential tool for its proof, it has been preannounced that another more direct way of proof will be published later. In fact, it is possible to give an alternative proof without any reference to the Villat-Stieltjes representation formula. Main purpose of the present paper is to fulfil the promise mentioned above. The present method is of primitive nature and is really an analogue of a classical proof in establishing the Schwarz-Christoffel formula for a function mapping a circle onto the exterior of a polygon. Moreover, a related formula for a function mapping an annulus onto a rectilinear polygonal ring domain which does not contain the point at infinity has been already derived by a method which remains valid in the present case with less modification (cf. the proof of Theorem 4 in [I]). On the other hand, the paper [1] contains further results on mappings onto multiply connected circular polygonal domains. Supplementary remarks will be made below also to some of them.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1950-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128843061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Existence theorem of conformal mapping of doubly-connected domains 双连通域的保角映射的存在性定理
Kodai Mathematical Seminar Reports Pub Date : 1949-12-01 DOI: 10.2996/KMJ/1138833531
Yūsaku Komatu
{"title":"Existence theorem of conformal mapping of doubly-connected domains","authors":"Yūsaku Komatu","doi":"10.2996/KMJ/1138833531","DOIUrl":"https://doi.org/10.2996/KMJ/1138833531","url":null,"abstract":"","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1949-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127083012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Note sur les fonctions analytiques de plusieurs variables 注意几个变量的解析函数
Kodai Mathematical Seminar Reports Pub Date : 1949-12-01 DOI: 10.2996/KMJ/1138833536
Kiyoshi Oka
{"title":"Note sur les fonctions analytiques de plusieurs variables","authors":"Kiyoshi Oka","doi":"10.2996/KMJ/1138833536","DOIUrl":"https://doi.org/10.2996/KMJ/1138833536","url":null,"abstract":"","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1949-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129213456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
On integral Formulas of analytic functions of several complex variables and some related problems. 若干复变解析函数的积分公式及有关问题。
Kodai Mathematical Seminar Reports Pub Date : 1949-12-01 DOI: 10.2996/KMJ/1138833535
S. Hitotumatu
{"title":"On integral Formulas of analytic functions of several complex variables and some related problems.","authors":"S. Hitotumatu","doi":"10.2996/KMJ/1138833535","DOIUrl":"https://doi.org/10.2996/KMJ/1138833535","url":null,"abstract":"It is well known that an analytic function of one complex variable can be represented by Cauchy*s integral formula. The generalization of this formula to the case of several complex variables have been treated by S.Bergman, A.Well, K.Oka, S Bochner and many other authors. These expressions can be classified into two types % its integration manifolds are, in the one case, the 4ί distinguished boundary surfaces\", and in the other case, the whole boundary hypersurface. In this Note, we shall consider some relations between both types, and some related problems.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"167 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1949-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121130228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Remark on Galois theory of simple ring 关于简单环伽罗瓦理论的评述
Kodai Mathematical Seminar Reports Pub Date : 1900-01-01 DOI: 10.2996/KMJ/1138844639
A. Inatomi
{"title":"Remark on Galois theory of simple ring","authors":"A. Inatomi","doi":"10.2996/KMJ/1138844639","DOIUrl":"https://doi.org/10.2996/KMJ/1138844639","url":null,"abstract":"1. Bortfeld [1] proved the following: Let D be a division ring which has (left) finite dimensionality over a division subring L of D and we suppose that the center C of D is an infinite field. If L is the invariant ring of an automorphism ω of D, then, for each intermediate division subring T between L and A, there exists an automorphism p such that T is an invariant ring of p. Recently, Nagahara and Tominaga [2] extended this therorem to simple rings, in case the commutator of an invariant ring is a division ring. In this note, we shall prove that Nagahara and Tominaga's result is still valid in the case where the commutator is a simple ring.","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115622228","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Perfection of measure spaces and W*-algebras 测度空间与W*-代数的完备性
Kodai Mathematical Seminar Reports Pub Date : 1900-01-01 DOI: 10.2996/KMJ/1138843297
Z. Takeda
{"title":"Perfection of measure spaces and W*-algebras","authors":"Z. Takeda","doi":"10.2996/KMJ/1138843297","DOIUrl":"https://doi.org/10.2996/KMJ/1138843297","url":null,"abstract":"","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"158 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115682087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A note on the different of the composed field 关于所组成字段的不同的注释
Kodai Mathematical Seminar Reports Pub Date : 1900-01-01 DOI: 10.2996/KMJ/1138843605
Hiraku Tôyama
{"title":"A note on the different of the composed field","authors":"Hiraku Tôyama","doi":"10.2996/KMJ/1138843605","DOIUrl":"https://doi.org/10.2996/KMJ/1138843605","url":null,"abstract":"","PeriodicalId":318148,"journal":{"name":"Kodai Mathematical Seminar Reports","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115720358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 15
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