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1.
Bloch constants for planar harmonic mappings 总被引:3,自引:0,他引:3
Huaihui Chen P. M. Gauthier W. Hengartner 《Proceedings of the American Mathematical Society》2000,128(11):3231-3240
We give a lower estimate for the Bloch constant for planar harmonic mappings which are quasiregular and for those which are open. The latter includes the classical Bloch theorem for holomorphic functions as a special case. Also, for bounded planar harmonic mappings, we obtain results similar to a theorem of Landau on bounded holomorphic functions.
2.
给出了从典型域到单位球的全纯映射高阶Frchet导数的Schwarz-Pick估计,从而推广了单位球上全纯自映射Frchet导数的Schwarz-Pick估计以及单位圆盘上有界全纯函数高阶导数的Schwarz-Pick估计的结论. 相似文献
3.
引入第一类典型域R_I(m,n)上的全纯映照子族H_k(R_I(m,n)),当k→+∞时,该映照族就是R_I(m,n)上的局部双全纯映照族.建立了H_k(R_I(m,n))上的Bonk偏差定理.当k=1和k→+∞时,其结果分别都回到了FitzGerad和龚升关于典型域R_I(m,n)上的Bonk偏差定理.当m=n=1时,其结果又回到了Liu和Minda在单位圆盘上的偏差定理.应用偏差定理,给出了映照族H_k(R_I(m,n))上的Bloch常数估计,其结果补全了从k=1和k→+∞之间的R_I(m,n)上Bloch常数估计的所有结果,而且把单位球上的Bloch常数估计推广到R_I(m,n)上. 相似文献
4.
We show that holomorphic mappings of bounded type defined on Fréchet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem. 相似文献
5.
Guang Yuan Zhang 《Proceedings of the American Mathematical Society》2007,135(3):767-776
This note presents an intuitive method to study center families of periodic orbits of complex holomorphic differential equations near singularities, based on some iteration properties of fixed point indices. As an application of this method, we will prove Needham's theorem in a more general version.
6.
B. van Brunt Hong Oh Kim Gregory Derfel 《Journal of Mathematical Analysis and Applications》2010,368(1):350-357
The pantograph equation is perhaps one of the most heavily studied class of functional differential equations owing to its numerous applications in mathematical physics, biology, and problems arising in industry. This equation is characterized by a linear functional argument. Heard (1973) [10] considered a generalization of this equation that included a nonlinear functional argument. His work focussed on the asymptotic behaviour of solutions for a real variable x as x→∞. In this paper, we revisit Heard's equation, but study it in the complex plane. Using results from complex dynamics we show that any nonconstant solution that is holomorphic at the origin must have the unit circle as a natural boundary. We consider solutions that are holomorphic on the Julia set of the nonlinear argument. We show that the solutions are either constant or have a singularity at the origin. There is a special case of Heard's equation that includes only the derivative and the functional term. For this case we construct solutions to the equation and illustrate the general results using classical complex analysis. 相似文献
7.
Maria Karmanova 《Journal of Functional Analysis》2008,254(5):1410-1447
We study Lipschitz mappings defined on an Hn-rectifiable metric space with values in an arbitrary metric space. We find necessary and sufficient conditions on the image and the preimage of a mapping for the validity of the coarea formula. As a consequence, we prove the coarea formula for some classes of mappings with Hk-σ-finite image. We also obtain a metric analog of the Implicit Function Theorem. All these results are extended to large classes of mappings with values in a metric space, including Sobolev mappings and BV-mappings. 相似文献
8.
9.
《复变函数与椭圆型方程》2012,57(9):797-801
The article deals with initial value problems of type δw/δt = Fw, w(0, ·) = φ where t is the time and F is a linear first order operator acting in the z = x ? iy-plane. In view of the classical Cauchy-Kovalevkaya Theorem, the initial value problem is solvable provided F has holomorphic coefficients and the initial function is holomorphic. On the other hand, the Lewy example [H. Lewy (1957). An example of a smooth linear partial differential equation without solution. Ann. of Math., 66, 155–158.] shows that there are equations of the above form with infinitely differentiable coefficients not having any solutions. The article in hand constructs, conversely, all linear operators F for which the initial value problem with an arbitrary holomorphic initial function is always solvable. In particular, we shall see that there are equations of that type whose coefficients are only continuous. 相似文献
10.
AMS(MOS): 46F10 We give an integral representation formula for entire holomorphic solutions of exponential type to systems of convolution equations. 相似文献
11.
Estela Ana Gavosto 《Journal of Geometric Analysis》1998,8(3):433-440
We prove the existence of infinitely many attracting basins for some holomorphic mappings in ℙ2. We also show that if a family of mappings has a complex generic homoclinic tangency, then some of the mappings in the family
have an attractive periodic fixed point. 相似文献
12.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1998,326(9):1063-1068
In this Note, we developp a new technic to study the existence of proper holomorphic mappings between a strictly pseudoconvex domain and certain special non-regular domains in ℂn. In particular, it can be applied in the case of the minimal ball and the Lie ball. We prove that self-proper holomorphic mappings between such domains are biholomorphic. Furthermore, we establish a necessary and sufficient condition to factorize a proper holomorphic mapping by automorphisms. Scaling method is applied for the first time in a singular points of the boundary of the domains. 相似文献
13.
I. A. Mednykh 《Siberian Mathematical Journal》2012,53(2):259-273
We obtain an upper bound for the number of holomorphic mappings of a genus 3 Riemann surface onto a genus 2 Riemann surface
in a series of cases. In particular, we establish that the number of holomorphic mappings of an arbitrary genus 3 Riemann
surface onto an arbitrary genus 2 Riemann surface is at most 48. We show that this estimate is sharp and find pairs of Riemann
surfaces for which it is attained. 相似文献
14.
Geoffrey Mason 《The Ramanujan Journal》2008,17(3):405-427
15.
The paper deals with a non–linear singular partial differential equation in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by Gérard –Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case. 相似文献
16.
Xianghong Gong 《Mathematische Annalen》2002,323(2):227-257
We show that reversible holomorphic mappings of have periodic points accumulating at an elliptic fixed point of general type. On the contrary, we also show the existence
of holomorphic symplectic mappings that have no periodic points of certain periods in a sequence of deleted balls about an
elliptic fixed point of general type. The radii of the balls are carefully chosen in terms of the periods, which allows us
to show the existence of holomorphic mappi
ngs of that are not reversible with respect to any involution with a holomorphic linear part, and that admit no invariant totally real and real surfaces.
Received: 5 December 2000 / Published online: 4 April 2002 相似文献
17.
A. M. Sinev 《Theoretical and Mathematical Physics》2009,158(3):377-390
We consider a solvable problem describing the dynamics of a quantum oscillator interacting with an electromagnetic field,
a classical force, and a heat bath. We propose a general method for solving Markovian master equations, the method of quantum
trajectories. We construct the stochastic evolution operator involving the stochastic analogue of the Baker-Hausdorff formula
and calculate the system density matrix for an arbitrary initial state. As a physical application, we evaluate the influence
of the environment at a finite temperature on the accuracy of measuring a weak classical force by the interference method.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 444–459, March, 2009. 相似文献
18.
K.-D. Kirchberg 《Annals of Global Analysis and Geometry》1999,17(2):97-111
In the first part of this paper, the closed spin Kähler manifolds of positive scalar curvature with smallest possible first eigenvalue of the Dirac operator, are characterized by holomorphic spinors. In the second part, the space of holomorphic spinors on a Kähler–Einstein manifold is described by eigenspinors of the square of the Dirac operator and vanishing theorems for holomorphic spinors are proved. 相似文献
19.
Seán Dineen 《Indagationes Mathematicae》2008,19(3):379-389
In this article we show that the pointwise existence of a regulariser for holomorphic Fredhom-valued mappings defined on pseudo-convex domains in Banach spaces with an unconditional basis implies the existence of a holomorphic regulariser. 相似文献
20.
Two differential operators which act on holomorphic mappings to complex projective space are studied. One operator is of second order and characterizes projective linear mappings. The other operator is of third order and may be viewed as a curvature. The two operators together play a role analogous to the Schwarzian derivative.A canonical approximation to a holomorphic mapping is defined, and a relationship between the approximation and the operators is derived. In the one variable case, this reduces to a classical result relating the Schwarzian derivative and the best Möbius approximation to a holomorphic function. 相似文献