The Malliavin calculus for functionals of a Poisson random measure has been developed by many authors. Bismut [2] has generalized the Malliavin calculus for Wiener-Poisson functionals by using the Girsanov theorem. As another method, in Bichteler, Gravereaux and Jacod [1], one can find the study of the Malliavin operator on Wiener-Poisson space and application of it to stochastic differential equations. Both in these works, the authors have given differential operators on Wiener-Poisson space and have proved the integration by parts formulas. These formulation suffers some limitation on an intensity measure, that is, the intensity measure must have a smooth density. On the other hand, in the Malliavin calculus for Wiener functionals, Wiener chaos expansion of the space of square integrable Wiener functionals can be considered as a Fock space, and the differential operator is regarded as the annihilation operator on a Fock space. This sort of structure can be also found in the case of the space of square integrable functionals of Wiener-Poisson space, see [6]. Nualart and Vives [10], [11], and Picard [13] have studied the annihilation operator and its dual operator (the creation operator) on the space of square integrable functionals of a Poisson random measure. Picard [12] has also given a smoothness criterion by using the duality formula (see Theorem 2.1) for functionals of a Poisson random measure under the Condition 1 (see Section 2) on the intensity measure, and has studied the solution to some stochastic differential equation. This argument of Picard can be generalized for some Wiener-Poisson functionals, see [5]. The Condition 1 differs from that of [1], and allows us to take a intensity measure with some singularity. One can find some interesting examples satisfying Condition 1, for instance, stable processes and CGMY processes (see [3]). The purpose of this paper is to prove the asymptotic expansion theorem (done in the Wiener space by Watanabe [18]) for functionals of a Poisson random measure. By using the Malliavin operator which we mentioned above, Sakamoto and Yoshida [15] have studied asymptotic expansion formulas of some
{"title":"Asymptotic expansions for functionals of a Poisson random measure","authors":"Masafumi Hayashi","doi":"10.1215/KJM/1250280977","DOIUrl":"https://doi.org/10.1215/KJM/1250280977","url":null,"abstract":"The Malliavin calculus for functionals of a Poisson random measure has been developed by many authors. Bismut [2] has generalized the Malliavin calculus for Wiener-Poisson functionals by using the Girsanov theorem. As another method, in Bichteler, Gravereaux and Jacod [1], one can find the study of the Malliavin operator on Wiener-Poisson space and application of it to stochastic differential equations. Both in these works, the authors have given differential operators on Wiener-Poisson space and have proved the integration by parts formulas. These formulation suffers some limitation on an intensity measure, that is, the intensity measure must have a smooth density. On the other hand, in the Malliavin calculus for Wiener functionals, Wiener chaos expansion of the space of square integrable Wiener functionals can be considered as a Fock space, and the differential operator is regarded as the annihilation operator on a Fock space. This sort of structure can be also found in the case of the space of square integrable functionals of Wiener-Poisson space, see [6]. Nualart and Vives [10], [11], and Picard [13] have studied the annihilation operator and its dual operator (the creation operator) on the space of square integrable functionals of a Poisson random measure. Picard [12] has also given a smoothness criterion by using the duality formula (see Theorem 2.1) for functionals of a Poisson random measure under the Condition 1 (see Section 2) on the intensity measure, and has studied the solution to some stochastic differential equation. This argument of Picard can be generalized for some Wiener-Poisson functionals, see [5]. The Condition 1 differs from that of [1], and allows us to take a intensity measure with some singularity. One can find some interesting examples satisfying Condition 1, for instance, stable processes and CGMY processes (see [3]). The purpose of this paper is to prove the asymptotic expansion theorem (done in the Wiener space by Watanabe [18]) for functionals of a Poisson random measure. By using the Malliavin operator which we mentioned above, Sakamoto and Yoshida [15] have studied asymptotic expansion formulas of some","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"91-132"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088253","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}
Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .
设P是对所有j∈[1,d−1]由可逆矩阵(a ij) di,j =1, dj = 0定义的PGL(d, C)的极大抛物子群。取PGL(d, C) /P型全纯抛物几何(M, exp， ω)。假设M是一个复射影流形。我们证明了:如果存在一个非常全纯映射f: CP 1−→M，则M对射影空间CP d−1是生物全纯的。
{"title":"On parabolic geometry of type PGL(d,C)/P","authors":"I. Biswas","doi":"10.1215/KJM/1250271316","DOIUrl":"https://doi.org/10.1215/KJM/1250271316","url":null,"abstract":"Let P be the maximal parabolic subgroup of PGL( d, C ) defined by invertible matrices ( a ij ) di,j =1 with a dj = 0 for all j ∈ [1 , d − 1]. Take a holomorphic parabolic geometry ( M, E P , ω ) of type PGL( d, C ) /P . Assume that M is a complex projective manifold. We prove the following: If there is a nonconstant holomorphic map f : CP 1 −→ M , then M is biholomorphic to the projective space CP d − 1 .","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"747-755"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087809","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}
This work is a continuation of the papers [BZ1] and [BZ2]. Here we prove some estimates for the sum of codimensions of singularities of affine planar rational curves. Acknowledgements. We want to thank Mariusz Koras, Zbigniew Je-lonek, Stepan Orevkov and Peter Russell for their interest in our work and interesting discussions.
本工作是论文[BZ1]和[BZ2]的延续。本文证明了仿射平面有理曲线奇点余维数和的一些估计。致谢我们要感谢Mariusz Koras, Zbigniew Je-lonek, Stepan Orevkov和Peter Russell对我们的工作和有趣的讨论感兴趣。
{"title":"Complex algebraic plane curves via Poincaré--Hopf formula. III. Codimension bounds","authors":"Maciej Borodzik, H. Zoladek","doi":"10.1215/KJM/1250271383","DOIUrl":"https://doi.org/10.1215/KJM/1250271383","url":null,"abstract":"This work is a continuation of the papers [BZ1] and [BZ2]. Here we prove some estimates for the sum of codimensions of singularities of affine planar rational curves. Acknowledgements. We want to thank Mariusz Koras, Zbigniew Je-lonek, Stepan Orevkov and Peter Russell for their interest in our work and interesting discussions.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"529-570"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088100","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}
{"title":"Homotopy cofibres, higher coassociativity and homotopy coalgebras","authors":"M. Golasiński, A. Murillo","doi":"10.1215/KJM/1250271387","DOIUrl":"https://doi.org/10.1215/KJM/1250271387","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"631-638"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088288","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}
{"title":"A computation of universal weight function for quantum affine algebra $U_q(widehat{mathfrak{gl}}_N)$","authors":"S. Khoroshkin, S. Pakuliak","doi":"10.1215/KJM/1250271413","DOIUrl":"https://doi.org/10.1215/KJM/1250271413","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"277-321"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250271413","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088435","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}
{"title":"The global profile of blow-up at space infinity in semilinear heat equations","authors":"M. Shimojo","doi":"10.1215/KJM/1250271415","DOIUrl":"https://doi.org/10.1215/KJM/1250271415","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"339-361"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250271415","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088504","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}
In the stable homotopy group πpnq+(p+1)q−1(V (1)) of the SmithToda spectrum V (1), the author constructed an essential element n for n ≥ 3 at the prime greater than three. Let β∗ s ∈ [V (1), S]spq+(s−1)q−2 denote the dual of the generator β′′ s ∈ πs(p+1)q(V (1)), which defines the β-element βs. In this paper, the author shows that the composite α1β1ξs ∈ πpnq+(s+1)pq+sq−6(S) for 1 < s < p − 2 is non-trivial, where ξs = β ∗ s−1 n ∈ πpnq+spq+(s−1)q−3(S) and q = 2(p − 1). As a corollary, ξs, α1ξs and β1ξs are also non-trivial for 1 < s < p − 2.
在SmithToda谱V(1)的稳定同伦群πpnq+(p+1)q−1(V(1))中，在n≥3的素数处构造了一个本质元n。设β * s∈[V (1)， s]spq+(s−1)q−2表示生成子β ' s∈πs(p+1)q(V(1))的对偶，它定义了β-元素βs。本文证明了复合α1β1ξ∈πpnq+(s+1)pq+sq−6(s)对于1 < s < p−2是非平凡的，其中ξ = β∗s−1 n∈πpnq+spq+(s−1)q−3(s)和q = 2(p−1)。作为推论，对于1 < s < p−2，ξ、α1ξ和β1ξ也是非平凡的。
{"title":"Some infinite elements in the Adams spectral sequence for the sphere spectrum","authors":"X. Liu","doi":"10.1215/KJM/1250271386","DOIUrl":"https://doi.org/10.1215/KJM/1250271386","url":null,"abstract":"In the stable homotopy group πpnq+(p+1)q−1(V (1)) of the SmithToda spectrum V (1), the author constructed an essential element n for n ≥ 3 at the prime greater than three. Let β∗ s ∈ [V (1), S]spq+(s−1)q−2 denote the dual of the generator β′′ s ∈ πs(p+1)q(V (1)), which defines the β-element βs. In this paper, the author shows that the composite α1β1ξs ∈ πpnq+(s+1)pq+sq−6(S) for 1 < s < p − 2 is non-trivial, where ξs = β ∗ s−1 n ∈ πpnq+spq+(s−1)q−3(S) and q = 2(p − 1). As a corollary, ξs, α1ξs and β1ξs are also non-trivial for 1 < s < p − 2.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"617-629"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088227","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}
{"title":"Effective calculation of the geometric height and the Bogomolov conjecture for hyperelliptic curves over function fields","authors":"K. Yamaki","doi":"10.1215/KJM/1250271420","DOIUrl":"https://doi.org/10.1215/KJM/1250271420","url":null,"abstract":"","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"48 1","pages":"401-443"},"PeriodicalIF":0.0,"publicationDate":"2008-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1250271420","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66088593","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}
Let A be a commutative noetherian ring. In this paper, we interpret localizing subcategories of the derived category of A by using subsets of Spec A and subcategories of the category of A-modules. We unify theorems of Gabriel, Neeman and Krause.
{"title":"On localizing subcategories of derived categories","authors":"Ryo Takahashi","doi":"10.1215/KJM/1265899482","DOIUrl":"https://doi.org/10.1215/KJM/1265899482","url":null,"abstract":"Let A be a commutative noetherian ring. In this paper, we interpret localizing subcategories of the derived category of A by using subsets of Spec A and subcategories of the category of A-modules. We unify theorems of Gabriel, Neeman and Krause.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"771-783"},"PeriodicalIF":0.0,"publicationDate":"2007-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1215/KJM/1265899482","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66114261","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}
This paper is devoted to study of sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extension of some results for entire functions to meromorphic functions. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic functions with at least one of them being transcendental can be also investigated in terms of the argument of this paper.
{"title":"Non-existence of unbounded fatou components of a meromorphic function","authors":"Zheng Jian-Hua, P. Niamsup","doi":"10.1215/KJM/1248983027","DOIUrl":"https://doi.org/10.1215/KJM/1248983027","url":null,"abstract":"This paper is devoted to study of sufficient conditions under which a transcendental meromorphic function has no unbounded Fatou components and to extension of some results for entire functions to meromorphic functions. Actually, we shall mainly discuss non-existence of unbounded wandering domains of a meromorphic function. The case for a composition of finitely many meromorphic functions with at least one of them being transcendental can be also investigated in terms of the argument of this paper.","PeriodicalId":50142,"journal":{"name":"Journal of Mathematics of Kyoto University","volume":"49 1","pages":"1-12"},"PeriodicalIF":0.0,"publicationDate":"2007-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66087619","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}
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