Canadian Mathematical Society www.cms.math.ca
 location:  Publications → journals
Search results

Search: All articles in the CJM digital archive with keyword holomorphic

 Expand all        Collapse all Results 1 - 12 of 12

1. CJM 2014 (vol 67 pp. 241)

Agler, Jim; McCarthy,
 Global Holomorphic Functions in Several Noncommuting Variables We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions. Keywords:noncommutative analysis, free holomorphic functionsCategory:15A54

2. CJM 2014 (vol 66 pp. 961)

Baird, Thomas
 Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's Yang-Mills over a Riemann Surface'' to compute $\mathbb Z/2$-Betti numbers of these spaces. Keywords:cohomology of moduli spaces, holomorphic vector bundlesCategories:32L05, 14P25

3. CJM 2012 (vol 64 pp. 318)

Ingram, Patrick
 Cubic Polynomials with Periodic Cycles of a Specified Multiplier We consider cubic polynomials $f(z)=z^3+az+b$ defined over $\mathbb{C}(\lambda)$, with a marked point of period $N$ and multiplier $\lambda$. In the case $N=1$, there are infinitely many such objects, and in the case $N\geq 3$, only finitely many (subject to a mild assumption). The case $N=2$ has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field $\bigcup_{n\geq 1}\mathbb{C}(\lambda^{1/n})$. Keywords:cubic polynomials, periodic points, holomorphic dynamicsCategory:37P35

4. CJM 2010 (vol 63 pp. 241)

Essouabri, Driss; Matsumoto, Kohji; Tsumura, Hirofumi
 Multiple Zeta-Functions Associated with Linear Recurrence Sequences and the Vectorial Sum Formula We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical sum formula can be deduced. Keywords:Zeta-functions, holomorphic continuation, recurrence sequences, Fibonacci numbers, sum formulasCategories:11M41, 40B05, 11B39

5. CJM 2009 (vol 61 pp. 566)

Graham, Ian; Hamada, Hidetaka; Kohr, Gabriela; Pfaltzgraff, John A.
 Convex Subordination Chains in Several Complex Variables In this paper we study the notion of a convex subordination chain in several complex variables. We obtain certain necessary and sufficient conditions for a mapping to be a convex subordination chain, and we give various examples of convex subordination chains on the Euclidean unit ball in $\mathbb{C}^n$. We also obtain a sufficient condition for injectivity of $f(z/\|z\|,\|z\|)$ on $B^n\setminus\{0\}$, where $f(z,t)$ is a convex subordination chain over $(0,1)$. Keywords:biholomorphic mapping, convex mapping, convex subordination chain, Loewner chain, subordinationCategories:32H02, 30C45

6. CJM 2007 (vol 59 pp. 3)

Biller, Harald
 Holomorphic Generation of Continuous Inverse Algebras We study complex commutative Banach algebras (and, more generally, continuous inverse algebras) in which the holomorphic functions of a fixed $n$-tuple of elements are dense. In particular, we characterize the compact subsets of~$\C^n$ which appear as joint spectra of such $n$-tuples. The characterization is compared with several established notions of holomorphic convexity by means of approximation conditions. Keywords:holomorphic functional calculus, commutative continuous inverse algebra, holomorphic convexity, Stein compacta, meromorphic convexity, holomorphic approximationCategories:46H30, 32A38, 32E30, 41A20, 46J15

7. CJM 2006 (vol 58 pp. 262)

Biswas, Indranil
 Connections on a Parabolic Principal Bundle Over a Curve The aim here is to define connections on a parabolic principal bundle. Some applications are given. Keywords:parabolic bundle, holomorphic connection, unitary connectionCategories:53C07, 32L05, 14F05

8. CJM 2005 (vol 57 pp. 871)

Zhang, Xi
 Hermitian Yang-_Mills--Higgs Metrics on\\Complete KÃ¤hler Manifolds In this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact K\"ahler manifolds. Keywords:vortex equation, Hermitian Yang--Mills--Higgs metric,, holomorphic vector bundle, KÃ¤hler manifoldsCategories:58E15, 53C07

9. CJM 2003 (vol 55 pp. 1100)

Khesin, Boris; Rosly, Alexei
 Polar Homology For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar $k$-chains are subvarieties of complex dimension $k$ with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincar\'e residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions. Keywords:Poincar\' e residue, holomorphic linkingCategories:14C10, 14F10, 58A14

10. CJM 2000 (vol 52 pp. 695)

Carey, A.; Farber, M.; Mathai, V.
 Correspondences, von Neumann Algebras and Holomorphic $L^2$ Torsion Given a holomorphic Hilbertian bundle on a compact complex manifold, we introduce the notion of holomorphic $L^2$ torsion, which lies in the determinant line of the twisted $L^2$ Dolbeault cohomology and represents a volume element there. Here we utilise the theory of determinant lines of Hilbertian modules over finite von~Neumann algebras as developed in \cite{CFM}. This specialises to the Ray-Singer-Quillen holomorphic torsion in the finite dimensional case. We compute a metric variation formula for the holomorphic $L^2$ torsion, which shows that it is {\it not\/} in general independent of the choice of Hermitian metrics on the complex manifold and on the holomorphic Hilbertian bundle, which are needed to define it. We therefore initiate the theory of correspondences of determinant lines, that enables us to define a relative holomorphic $L^2$ torsion for a pair of flat Hilbertian bundles, which we prove is independent of the choice of Hermitian metrics on the complex manifold and on the flat Hilbertian bundles. Keywords:holomorphic $L^2$ torsion, correspondences, local index theorem, almost KÃ¤hler manifolds, von~Neumann algebras, determinant linesCategories:58J52, 58J35, 58J20

11. CJM 1998 (vol 50 pp. 547)

Gauthier, Paul M.
 Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds Cauchy and Poisson integrals over {\it unbounded\/} sets are employed to prove Mittag-Leffler type theorems with massive singularities as well as approximation theorems for holomorphic and harmonic functions. Keywords:holomorphic, harmonic, Mittag-Leffler, RungeCategories:30F99, 31C12

12. CJM 1997 (vol 49 pp. 1224)

Ørsted, Bent; Zhang, Genkai
 Tensor products of analytic continuations of holomorphic discrete series We give the irreducible decomposition of the tensor product of an analytic continuation of the holomorphic discrete series of $\SU(2, 2)$ with its conjugate. Keywords:Holomorphic discrete series, tensor product, spherical function, Clebsch-Gordan coefficient, Plancherel theoremCategories:22E45, 43A85, 32M15, 33A65
 top of page | contact us | privacy | site map |

© Canadian Mathematical Society, 2016 : https://cms.math.ca/