共查询到20条相似文献,搜索用时 578 毫秒
1.
Daniel Carando Verónica Dimant Santiago Muro 《Journal of Mathematical Analysis and Applications》2007,336(2):1324-1340
A result of Godefroy and Shapiro states that the convolution operators on the space of entire functions on Cn, which are not multiples of identity, are hypercyclic. Analogues of this result have appeared for some spaces of holomorphic functions on a Banach space. In this work, we define the space holomorphic functions associated to a sequence of spaces of polynomials and determine conditions on this sequence that assure hypercyclicity of convolution operators. Some known results come out as particular cases of this setting. We also consider holomorphic functions associated to minimal ideals of polynomials and to polynomials of the Schatten-von Neumann class. 相似文献
2.
Summary Our aim is to determine the precise space of functions for which the trapezoidal rule converges with a prescribed rate as the number of nodes tends to infinity. Excluding or controlling odd functions in some way it is possible to establish a correspondence between the speed of convergence and regularity properties of the function to be integrated. In this way we characterize Sobolev spaces, certain spaces of infinitely differentiable functions, of functions holomorphic in a strip, of entire functions of order greater than 1 and of entire functions of exponential type by the speed of convergence.Dedicated to Professor G. Hämmerlin on the occasion of his 60th birthday 相似文献
3.
Christer O. Kiselman 《中国科学 数学(英文版)》2017,60(6):1005-1018
We study solutions to convolution equations for functions with discrete support in R~n, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in C~n, and we determine possible domains in terms of the properties of the convolution operator. 相似文献
4.
We prove the existence of entire functions which are universal under translations and bounded on certain prescribed sets.
It is also shown that the family of all these universal functions is a dense but not a Gδ-subset in the space of entire functions provided with a natural metric.
Received: 24 November 2004; revised: 12 April 2005 相似文献
5.
Theorems of Wiman and Arima about entire holomorphic functions of a complex variable are generalized to the case of n—subharmonic
functions on spherical n-dimensional cones. 相似文献
6.
Fueter’s Theorem on the construction of monogenic quaternionic functions starting with a holomorphic function in the upper
half of the complex plane, is further generalized in a Clifford analysis setting. The result obtained contains previous generalizations
as special cases. 相似文献
7.
8.
The Titchmarsh convolution theorem is a celebrated result about the support of the convolution of two functions. We present a simple proof based on the canonical factorization theorem for bounded holomorphic functions on the unit disk.
相似文献9.
A regular extension phenomenon of functions defined on Euclidean space with values in a Clifford algebra was studied by Le
Hung Son in the 90’s using methods of Clifford analysis, a function theory which, is centred around the notion of a monogenic
function, i.e. a null solution of the firstorder, vector-valued Dirac operator in .
The isotonic Clifford analysis is a refinement of the latter, which arises for even dimension. As such it also may be regarded
as an elegant generalization to complex Clifford algebra-valued functions of both holomorphic functions of several complex
variables and two-sided biregular function theories.
The aim of this article is to present a Hartogs theorem on isotonic extendability of functions on a suitable domain of . As an application, the extension problem for holomorphic functions and so for the two-sided biregular ones is discussed.
相似文献
10.
We show that if a small holomorphic Sobolev space on the unit disk is not just small but very small, then a trivial necessary
condition is also sufficient for a composition operator to be bounded. A similar result for holomorphic Lipschitz spaces is
also obtained. These results may be viewed as boundedness analogues of Shapiro’s theorem concerning compact composition operators
on small spaces. We also prove the converse of Shapiro’s theorem if the symbol function is already contained in the space
under consideration. In the course of the proofs we characterize the bounded composition operators on the Zygmund class. Also,
as a by-product of our arguments, we show that small holomorphic Sobolev spaces are algebras. 相似文献
11.
Alexander Brudnyi 《Journal of Functional Analysis》2006,231(2):418-437
The classical integral representation formulas for holomorphic functions defined on pseudoconvex domains in Stein manifolds play an important role in the constructive theory of functions of several complex variables. In this paper, we will show how to construct similar formulas for certain classes of holomorphic functions defined on coverings of such domains. 相似文献
12.
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
13.
N. Tsirivas 《Archiv der Mathematik》2006,87(5):427-435
Let Ω be an unbounded simply connected domain in
satisfying some topological assumptions; for example let Ω be an open half-plane. We show that there exists a bounded holomorphic
function on Ω which extends continuously on
and is a universal Taylor series in Ω in the sense of Luh and Chui–Parnes with respect to any center. Our proof uses Arakeljan’s
Approximation Theorem.
Further we strengthen results of G. Costakis [2] concerning universal Taylor series with respect to one center in the sense
of Luh and Chui–Parnes in the complement G of a compact connected set. We prove that such functions can be smooth on the boundary of G and be zero at ∞. If the universal approximation is also valid on ∂G, then the function can not be smooth on ∂G, but it may vanish at ∞. Our results are generic in natural Fréchet spaces of holomorphic functions.
Received: 29 September 2005; revised: 21 February 2006 相似文献
14.
In this paper we establish an explicit relation between the growth type of general entire solutions to the generalized Cauchy-Riemann
system in
\mathbbRn+1{\mathbb{R}^{n+1}}
and their Taylor coefficients. This formula then enables us to compute the growth type of some higher dimensional generalizations
of the trigonometric and special functions that are null-solutions to this system. 相似文献
15.
V. V. Morzhakov 《Mathematical Notes》1974,16(3):846-851
We prove the solvability of convolution equations in some spaces of holomorphic functions of n variables. We clarify the structure of solutions of the homogeneous equation. 相似文献
16.
17.
C. L. Prather 《Numerical Functional Analysis & Optimization》2013,34(3-4):509-520
It is shown that if f is any entire function in the class [2,π/2), which along with finitely many of its successive derivatives, vanishes at the integer lattice points, suitably scaled, then f is identically zero. It is then shown that if f is any entire function in a proper subclass of [2,π/2), which along with finitely many of its successive derivatives, is bounded at the integer lattice points, suitably scaled, then f is constant. A heuristic argument in support of the conjecture that this latter result holds for the full class [2, π/2) is given. 相似文献
18.
Roman Lávička 《Advances in Applied Clifford Algebras》2007,17(3):549-554
In [7], B. Fuglede has proved that finely holomorphic functions on a finely open subset U of the complex plane C are finely locally extendable to usual continuously differentiable functions. We shall adopt B. Fuglede’s approach to show
that the same remains true even for functions which have only finely continuous fine differential on U. In higher dimensions, an analogous result may be obtained and the result can be applied to finely monogenic functions which
were introduced recently as a higher dimensional analogue of finely holomorphic functions.
I acknowledge the financial support from the grant GA 201/05/2117. This work is also a part of the research plan MSM 0021620839,
which is financed by the Ministry of Education of the Czech Republic. 相似文献
19.
We develop a constructive framework to define difference approximations of Dirac operators which factorize the discrete Laplacian.
This resulting notion of discrete monogenic functions is compared with the notion of discrete holomorphic functions on quad-graphs.
In the end Dirac operators on quad-graphs are constructed. 相似文献
20.
A new Cauchy-type formula for hypermonogenic functions is derived. Hypermonogenic functions, introduced in [6], are a generalization
of holomorphic functions to several dimensions. The power function xm is hypermonogenic.
This paper is dedicated to the memory of our friend and colleague Jarolim Bureš 相似文献