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1.
Maciej P. Denkowski 《Arkiv f?r Matematik》2009,47(1):73-89
In this paper we introduce Coleff–Herrera residue currents defined by systems of c-holomorphic functions and prove a Lelong–Poincaré
and a Cauchy-type formula as well as the transformation law for these currents. 相似文献
2.
Ricardo Abreu-Blaya Juan Bory-Reyes Michael Shapiro 《Complex Analysis and Operator Theory》2007,1(2):143-168
In this paper we discuss the notion of the Bochner–Martinelli kernel for domains with rectifiable boundary in
, by expressing the kernel in terms of the exterior normal due to Federer (see [17,18]). We shall use the above mentioned
kernel in order to prove both Sokhotski–Plemelj and Plemelj–Privalov theorems for the corresponding Bochner–Martinelli integral,
as well as a criterion of the holomorphic extendibility in terms of the representation with Bochner–Martinelli kernel of a
continuous function of two complex variables.
Explicit formula for the square of the Bochner–Martinelli integral is rediscovered for more general surfaces of integration
extending the formula established first by Vasilevski and Shapiro in 1989.
The proofs of all these facts are based on an intimate relation between holomorphic function theory of two complex variables
and some version of quaternionic analysis.
Submitted: September 6, 2006. Accepted: November 1, 2006. 相似文献
3.
Residue currents with prescribed annihilator ideals 总被引:1,自引:0,他引:1
Mats Andersson Elizabeth Wulcan 《Annales Scientifiques de l'école Normale Supérieure》2007,40(6):985-1007
Given a coherent ideal sheaf J we construct locally a vector-valued residue current R whose annihilator is precisely the given sheaf. In case J is a complete intersection, R is just the classical Coleff–Herrera product. By means of these currents we can extend various results, previously known for a complete intersection, to general ideal sheaves. Combining with integral formulas we obtain a residue version of the Ehrenpreis–Palamodov fundamental principle. 相似文献
4.
LiangYuLIN ChunHuiQIU 《数学学报(英文版)》2004,20(6):989-998
Suppose that D is a bounded domain with a piecewise C^1 smooth boundary in C^n. Let ψ∈C^1 α(δD). By using the Hadamard principal value of the higher order singular integral and solid angle coefficient method of points on the boundary, we give the Plemelj formula of the higher order singular integral with the Boehner-Martinelli kernel, which has integral density ψ. Moreover, by means of the Plemelj formula and methods of complex partial differential equations, we discuss the corresponding Cauehy boundary value problem with the Boehner-Martinelli kernel on a closed piecewise smooth manifold and obtain its unique branch complex harmonic solution. 相似文献
5.
This paper deals with the boundary value properties and the higher order singular integro-differential equation. On Stein
manifolds, the Hadamard principal value, the Plemelj formula and the composite formula for higher order Bochner–Martinelli
type integral are given. As an application, the composite formula is used for discussing the solution of the higher order
singular integro-differential equation. 相似文献
6.
Given a free resolution of an ideal a of holomorphic functions, one can construct a vector-valued residue current R , which coincides with the classical Coleff–Herrera product if a is a complete intersection ideal and whose annihilator ideal is precisely a. 相似文献
7.
Elizabeth Wulcan 《Arkiv f?r Matematik》2007,45(1):157-178
With a given holomorphic section of a Hermitian vector bundle, one can associate a residue current by means of Cauchy–Fantappiè–Leray
type formulas. In this paper we define products of such residue currents. We prove that, in the case of a complete intersection,
the product of the residue currents of a tuple of sections coincides with the residue current of the direct sum of the sections. 相似文献
8.
Mats Andersson 《Mathematische Zeitschrift》2006,254(2):315-332
Let f be a r×m-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic
ψ such that ϕ=f
ψ, provided that ϕ is holomorphic and annihilates a certain residue current with support on the set where f is not surjective. We also consider formulas for interpolation. As applications we obtain generalizations of various results
previously known for the case r=1.
The author was partially supported by the Swedish Research Council 相似文献
9.
Håkan Samuelsson 《Arkiv f?r Matematik》2009,47(1):127-141
Let X be a complex manifold and let f:X→ℂ
p
be a holomorphic mapping defining a complete intersection. We prove that the iterated Mellin transform of the residue integral
associated with f has an analytic continuation to a neighborhood of the origin in ℂ
p
. 相似文献
10.
Lan Zhe LIU Shan Zhen LU 《数学学报(英文版)》2006,22(1):69-76
Let Baδ^A. be the maxiamal multilinear Bochner-Riesz operators generated by Bochner Riesz operators and D^αA∈ Lipβ(|α|= m), The continuity of the operator on some Hardy and Herz type Hardy is obtained. 相似文献
11.
The Rankin–Cohen product of two modular forms is known to be a modular form. The same formula can be used to define the Rankin–Cohen
product of two holomorphic functions f and g on the upper half-plane. Assuming that this product is a modular form, we prove that both f and g are modular forms if one of them is. We interpret this result in terms of solutions of linear ordinary differential equations. 相似文献
12.
We investigate connections between radial Fourier multipliers on ℝ
d
and certain conical Fourier multipliers on ℝ
d+1. As an application we obtain a new weak type endpoint bound for the Bochner–Riesz multipliers associated with the light cone
in ℝ
d+1, where d≥4, and results on characterizations of L
p
→L
p,ν inequalities for convolutions with radial kernels. 相似文献
13.
Mihai Cristea 《Complex Analysis and Operator Theory》2011,5(3):863-880
The paper continues the work of Royster (Duke Math J 19:447–457, 1952), Mocanu [Mathematica (Cluj) 22(1):77–83, 1980; Mathematica
(Cluj) 29:49–55, 1987], Cristea [Mathematica (Cluj) 36(2):137–144, 1994; Complex Var 42:333–345, 2000; Mathematica (Cluj)
43(1):23–34, 2001; Mathematica (Cluj), 2010, to appear; Teoria Topologica a Functiilor Analitice, Editura Universitatii Bucuresti,
Romania, 1999] of extending univalence criteria for complex mappings to C
1 mappings. We improve now the method of Loewner chains which is usually used in complex univalence theory for proving univalence
criteria or for proving quasiconformal extensions of holomorphic mappings f : B → C
n
to C
n
. The results are surprisingly strong. We show that the usual results from the theory, like Becker’s univalence criteria remain
true for C
1 mappings and since we use a stronger form of Loewner’s theory, we obtain results which are stronger even for holomorphic
mappings f : B → C
n
. In our main result (Theorem 4.1) we end the researches dedicated to quasiconformal extensions of K-quasiregular and holomorphic mappings f : B → C
n
to C
n
. We show that a C
1 quasiconformal map f : B → C
n
can be extended to a quasiconformal map F : C
n
→ C
n
, without any metric condition imposed to the map f. 相似文献
14.
We discuss in Sect. 1 the property of regularity at the boundary of separately holomorphic functions along families of discs
and apply, in Sect. 2, to two situations. First, let W\mathcal{W} be a wedge of ℂ
n
with C
ω
, generic edge ℰ: a holomorphic function f on W\mathcal{W} has always a generalized (hyperfunction) boundary value bv(f) on ℰ, and this coincides with the collection of the boundary values along the discs which have C
ω
transversal intersection with ℰ. Thus Sect. 1 can be applied and yields the uniform continuity at ℰ of f when bv(f) is (separately) continuous. When W\mathcal{W} is only smooth, an additional property, the temperateness of f at ℰ, characterizes the existence of boundary value bv(f) as a distribution on ℰ. If bv(f) is continuous, this operation is consistent with taking limits along discs (Theorem 2.8). By Sect. 1, this yields again
the uniform continuity at ℰ of tempered holomorphic functions with continuous bv. This is the theorem by Rosay (Trans. Am. Math. Soc. 297(1):63–72, 1986), in whose original proof the method of “slicing” by discs is not used. 相似文献
15.
Mats Andersson 《Arkiv f?r Matematik》2005,43(2):201-219
LetZ be the zero set of a holomorphic sectionf of a Hermitian vector bundle. It is proved that the current of integration over the irreducible components ofZ of top degree, counted with multiplicities, is a product of a residue factorR
f
and a “Jacobian factor”. There is also a relation to the Monge-Ampère expressions (dd
c
log|f|)
k
, which we define for all positive powersk.
The author was partially supported by the Swedish Research Council. 相似文献
16.
V. V. Savchuk 《Ukrainian Mathematical Journal》2007,59(9):1397-1407
We investigate the problem of approximation of functions ƒ holomorphic in the unit disk by means A
ρ, r
(f) as ρ → 1−. In terms of the error of approximation by these means, a constructive characteristic of classes of holomorphic
functions H
p
r
Lipα is given. The problem of the saturation of A
ρ, r
(f) in the Hardy space H
p
is solved.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 9, pp. 1253–1260, September, 2007. 相似文献
17.
We study interpolating sequences in the unit ball for A–pwith p > 0, the Banach space of holomorphic functions f with(1 – |z|2)p |f(z)| bounded. The finite unions of A–p-interpolatingsequences are characterized by a Carleson type condition. 相似文献
18.
We prove the equivalence of special moduli of smoothness and K-functionals of fractional order in the space H
p
, p > 0. As applications, we obtain an analog of the Hardy–Littlewood theorem and the sharp estimates of the rate of approximation
of functions by generalized Bochner–Riesz means. 相似文献
19.
De Yu Zhang 《数学学报(英文版)》2009,25(6):945-960
In this paper we prove zero-density estimates of the large sieve type for the automorphic L-function L(s, f × χ), where f is a holomorphic cusp form and χ(mod q) is a primitive character. 相似文献
20.
A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth,
distortion, curvature and covering theorems for B∞(α).
Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation.
Research supported in part by a National Science Foundation grant. 相似文献