共查询到20条相似文献,搜索用时 46 毫秒
1.
《复变函数与椭圆型方程》2012,57(3):247-261
In this article, vector-valued holomorphic and meromorphic functions on a Riemann surface to a complete Hausdorff locally semi-convex space are discussed. By introducing the concepts of vector-valued holomorphic and meromorphic differential forms, Cauchy's theorem and the Residue theorem of a vector-valued differential form on a Riemann surface are proved. Using the theory on the operator and the theory of a cohomology of a sheaf, we give a proof of the Mittag-Leffler theorem for vector-valued meromorphic functions on a non-compact Riemann surface to a complete Hausdorff locally semi-convex space. 相似文献
2.
《复变函数与椭圆型方程》2012,57(2):111-118
In this article, we prove a unicity theorem of meromorphic functions sharing three values, which is an improvement of the theorem given by Terglane. Some examples show that the result in this article is best possible. 相似文献
3.
《复变函数与椭圆型方程》2012,57(12):1085-1095
In this article we give complete characterizations of shift-invariant uniform algebras AS on compact abelian groups, in which two of the classical theorems for analytic functions hold, namely, Radó's theorem for analytic extension and Riemann's theorem for removable singularities. Our characterization is in terms of algebraical properties of the semigroup S of non-zero Fourier coefficients of the functions in AS . 相似文献
4.
《复变函数与椭圆型方程》2012,57(2):161-164
We prove a gap theorem and the “Fatou change-of-sign theorem” [Fatou, P., 1906, Sèries trigonométriques e séries de Taylor. Acta Mathematica, 39, 335–400] for expansions in common Schauder basis of holomorphic functions. 相似文献
5.
《复变函数与椭圆型方程》2012,57(10):915-928
In this paper, we obtain Cauchy's integral formula on certain distinguished boundary for functions with values in a universal Clifford algebra, which is similar to the classical Cauchy's integral formula on the distinguished boundary of polycylinder for several complex variables. By using it, both the mean value theorem and the maximum modulus theorem are given. 相似文献
6.
In this paper, we mainly study the Rm (m>0) Riemann boundary value problems for functions with values in a Clifford algebra C?(V3, 3). We prove a generalized Liouville‐type theorem for harmonic functions and biharmonic functions by combining the growth behaviour estimates with the series expansions for k‐monogenic functions. We obtain the result under only one growth condition at infinity by using the integral representation formulas for harmonic functions and biharmonic functions. By using the Plemelj formula and the integral representation formulas, a more generalized Liouville theorem for harmonic functions and biharmonic functions are presented. Combining the Plemelj formula and the integral representation formulas with the above generalized Liouville theorem, we prove that the Rm (m>0) Riemann boundary value problems for monogenic functions, harmonic functions and biharmonic functions are solvable. Explicit representation formulas of the solutions are given. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
7.
Lou 《Applied Mathematics and Optimization》2008,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
8.
《Quaestiones Mathematicae》2013,36(1):59-66
Abstract In [2], Aupetit studied the perturbation of elements of a Banach algebra A by elements of an inessential ideal I of A. The main result of his paper is based on a lemma ([2], theorem 1.1) obtained by the use of subharmonic methods and analytic multivalued functions. Our aim in this note is to prove Auptetit's perturbation theorem ([2], theorem 2.4) by making use of elementary methods. 相似文献
9.
Lou 《Applied Mathematics and Optimization》2003,47(2):121-142
Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions
are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the
corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established. 相似文献
10.
Bogdan Szal 《Proceedings Mathematical Sciences》2010,120(5):563-582
We consider the embedding relation between the class W
q
H
β
ω
, including only odd functions and a set of functions defined via the strong means of Fourier series of odd continuous functions.
We establish an improvement of a recent theorem of Le and Zhou [Math. Inequal. Appl.
11(4) (2008) 749–756] which is a generalization of Tikhonov’s results [Anal. Math.
31 (2005) 183–194]. We also extend the Leindler theorem [Anal. Math.
31 (2005) 175–182] concerning sequences of Fourier coefficients. 相似文献
11.
《Quaestiones Mathematicae》2013,36(5):687-699
AbstractIn the paper, joint universality theorems for periodic zeta functions with multiplicative coefficients and periodic Hurwitz zeta-functions are proved. The main theorem of [11] is extended, and two new joint universality theorems on the approximation of a collection of analytic functions by discrete shifts of the above zeta-functions are obtained. For this, certain linear independence hypotheses are applied. 相似文献
12.
Douglas S. Bridges 《Archive for Mathematical Logic》2009,48(5):437-448
In the informal setting of Bishop-style constructive reverse mathematics we discuss the connection between the antithesis
of Specker’s theorem, Ishihara’s principle BD-N, and various types of equicontinuity. In particular, we prove that the implication from pointwise equicontinuity to uniform
sequential equicontinuity is equivalent to the antithesis of Specker’s theorem; and that, for a family of functions on a separable
metric space, the implication from uniform sequential equicontinuity to uniform equicontinuity is equivalent to BD-N.
相似文献
13.
《Quaestiones Mathematicae》2013,36(1-2):341-352
Abstract In this paper we show that a Banach-Dieudonné type theorem for the space of entire functions of bounded type on a Banach space only holds in the finite dimensional case. We also study if this result holds in the setting of Fréchet spaces. 相似文献
14.
In this paper we study the Riemann and Hilbert problems of k-monogenic functions. By using Euler operator, we transform the boundary value problem of k-monogenic functions into the boundary value problems of monogenic functions. Then by the Almansi-type theorem of k-monogenic functions, we get the solutions of these problems. 相似文献
15.
《复变函数与椭圆型方程》2012,57(5):429-440
We extend Newman and Keldysh theorems to the behavior of sequences of functions in Hp (μ) which explain geometric properties of discs in these spaces. Through Keldysh's theorem we obtain asymptotic results for extremal polynomials in Sobolev spaces. 相似文献
16.
We have established (see Shiohama and Xu in J. Geom. Anal. 7:377–386, 1997; Lemma) an integral formula on the absolute Lipschitz-Killing curvature and critical points of height functions of an isometrically
immersed compact Riemannian n-manifold into R
n+q
. Making use of this formula, we prove a topological sphere theorem and a differentiable sphere theorem for hypersurfaces
with bounded L
n/2 Ricci curvature norm in R
n+1. We show that the theorems of Gauss-Bonnet-Chern, Chern-Lashof and the Willmore inequality are all its consequences. 相似文献
17.
《Optimization》2012,61(12):2139-2155
ABSTRACTBy using an implicit function theorem and a result of error bound, we provide new constraint qualifications ensuring the Karush–Kuhn–Tuker necessary optimality conditions for both smooth and nonsmooth optimization problems in normed spaces or Banach spaces. 相似文献
18.
Roberto Camporesi 《Acta Appl Math》2002,73(1-2):15-38
Recent results on the harmonic analysis of spinor fields on the complex hyperbolic space H
n
(C) are reviewed. We discuss the action of the invariant differential operators on the Poisson transforms, the theory of spherical functions and the spherical transform. The inversion formula, the Paley–Wiener theorem, and the Plancherel theorem for the spherical transform are obtained by reduction to Jacobi analysis on L
2(R). 相似文献
19.
Tiba 《Applied Mathematics and Optimization》2008,47(1):45-58
Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W
0
l,p
(Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary
value problems of arbitrary order, in arbitrary dimension and with general cost functionals. 相似文献
20.
We characterize Lp norms of functions onR
n for 1<p<∞ in terms of their Gabor coefficients. Moreover, we use the Carleson-Hunt theorem to show that the Gabor expansions
of Lp functions converge to the functions almost everywhere and in Lp for 1<p<∞. In L1 we prove an analogous result: the Gabor expansions converge to the functions almost everywhere and in L1 in a certain Cesàro sense. Consequently, we are able to establish that a large class of Gabor families generate Banach frames
for Lp (R
n) when 1≤p<∞. 相似文献