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1.
Alencar Raymundo; Aron Richard; Galindo Pablo; Zagorodnyuk Andriy 《Bulletin London Mathematical Society》2003,35(1):55-64
The authors study the algebra of uniformly continuous holomorphicsymmetric functions on the ball of lp, investigating in particularthe spectrum of such algebras. To do so, they examine the algebraof symmetric polynomials on lp-spaces, as well as finitely generatedsymmetric algebras of holomorphic functions. Such symmetricpolynomials determine the points in lp up to a permutation. 相似文献
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3.
On Weighted Spaces of Harmonic and Holomorphic Functions 总被引:8,自引:0,他引:8
Weighed spaces of harmonic and holomorphic functions on theunit disc are studied. We show that for all radial weights whichare not decreasing too fast the space of harmonic functionsis isomorphic to c0. For the weights that we consider we completelycharacterize those spaces of holomorphic functions which areisomorphic to c0. Moreover, we determine when the Riesz projection,mapping the weighted space of harmonic functions onto the correspondingspace of holomorphic functions, is bounded. 相似文献
4.
Let K be a kernel on Rn, that is, K is a non-negative, unboundedL1 function that is radially symmetric and decreasing. We definethe convolution K * F by
and note from Lp-capacity theory [11, Theorem 3] that, if F Lp, p > 1, then K * F exists as a finite Lebesgue integraloutside a set A Rn with CK,p(A) = 0. For a Borel set A,
where
We define the Poisson kernel for = {(x, y) : x Rn, y > 0} by
and set
Thus u is the Poisson integral of the potential f = K * F, andwe write u=Py*(K*F)=Py*f=P[f]. We are concerned here with the limiting behaviour of such harmonicfunctions at boundary points of , and in particular with the tangential boundary behaviour ofthese functions, outside exceptional sets of capacity zero orHausdorff content zero. 相似文献
5.
Ukrainian Mathematical Journal - We compute the exact values of the least upper bounds on the classes of bounded holomorphic and harmonic functions in a unit disk for the remainders in a... 相似文献
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The C*-algebra
generated by the Bergman and anti-Bergman projections and by the operators of multiplication by piecewise continuous functions on the Lebesgue space L2(Π) over the upper half-plane is studied. Making use of a local principle, limit operators techniques, and the Plamenevsky results on two-dimensional singular integral operators with coefficients admitting homogeneous discontinuities we reduce the study to simpler C*-algebras associated with points
and pairs
We construct a symbol calculus for unital C*-algebras generated by n orthogonal projections sum of which equals the unit and by m one-dimensional orthogonal projections. Such algebras are models of local algebras at points z ∈∂Π being the discontinuity points of coefficients. A symbol calculus for the C*- algebra
and a Fredholm criterion for the operators
are obtained. Finally, a C*-algebra isomorphism between the quotient algebra
where
is the ideal of compact operators, and its analogue
for the unit disk is constructed. 相似文献
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A Peak Point Theorem for Uniform Algebras Generated by Smooth Functions on Two-Manifolds 总被引:1,自引:0,他引:1
We establish the peak point conjecture for uniform algebrasgenerated by smooth functions on two-manifolds: if A is a uniformalgebra generated by smooth functions on a compact smooth two-manifoldM, such that the maximal ideal space of A is M, and every pointof M is a peak point for A, then A = C(M). We also give an alternativeproof in the case when the algebra A is the uniform closureP(M) of the polynomials on a polynomially convex smooth two-manifoldM lying in a strictly pseudoconvex hypersurface in Cn. 相似文献
10.
L. Yu. Cherednikova 《Mathematical Notes》2005,77(5-6):715-725
Suppose that
is a system of continuous subharmonic functions in the unit disk
and
is the class of holomorphic functions f in
such that log|f(z)| ≤ B
f
p
f
(z) + C
f
, z ∈
, where B
f
and C
f
are constants and p
f
∈
. We obtain sufficient conditions for a given number sequence Λ = { λn} ⊂
to be a subsequence of zeros of some nonzero holomorphic function from
, i.e., Λ is a nonuniqueness sequence for
.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 775–787.Original Russian Text Copyright ©2005 by L. Yu. Cherednikova. 相似文献
11.
We study the Jordan structures and geometry of bounded matrix-valued harmonic functions on a homogeneous space and their analogue, the harmonic functionals, in the setting of Fourier algebras of homogeneous spaces.Supported by EPSRC grant GR/G91182 and NSERC grant 7679. 相似文献
12.
We study homomorphisms between Fréchet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set. 相似文献
13.
Gary F. Birkenmeier Henry E. Heatherly Jin Yong Kim Jae Keol Park 《Acta Mathematica Hungarica》2002,95(1-2):101-114
Let
be a unital K-algebra, where K is a commutative ring with unity. An idempotent
is {\it left semicentral\/} if
, and
is {\it SCI-generated\/} if it is generated as a K-module by left semicentral idempotents. This paper develops the basic properties of SCI-generated algebras and characterizes those that are also prime, semiprime, primitive, or subdirectly irreducible. Minimal ideals and the socle of SCI-generated algebras are investigated. Conditions are found to describe a large class of SCI-generated algebras via generalized triangular matrix representations. SCI-generated piecewise domains are characterized. Examples are given that illustrate the breadth and diversity of the class of SCI-generated algebras. 相似文献
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Gabriella DiBlasio 《Semigroup Forum》1998,57(3):359-377
tA )t≥0 on X. We denote by XA(θ,p), for 0 < θ < 1, the interpolation spaces of X and D(A) introduced by Berens and Butzer in [1]. These spaces play an important
role in the approximation theory ( [2] ) as well as in the study of the abstract parabolic equation u′ (t) = Au(t) + f(t) ( [3] ). It has been proved in [6] that these spaces are meaningful (and still enjoy relevant properties) also in the case
θ = 0. In this paper we continue the study of [6] and prove new interesting properties of these spaces. 相似文献
16.
Hiroaki Terao 《Journal of Algebra》2002,250(2):549
Let Δ be a finite set of nonzero linear forms in several variables with coefficients in a field K of characteristic zero. Consider the K-algebra C(Δ) of rational functions generated by {1/α α Δ}. Then the ring ∂(V) of differential operators with constant coefficients naturally acts on C(Δ). We study the graded ∂(V)-module structure of C(Δ). We especially find standard systems of minimal generators and a combinatorial formula for the Poincaré series of C(Δ). Our proofs are based on a theorem by Brion–Vergne [4] and results by Orlik–Terao [9]. 相似文献
17.
The purpose of this note is to obtain precise information about associative or Jordan algebras generated by two idempotents. 相似文献
18.
In this paper, we study free holomorphic functions on the regular polyball, which was recently introduced by Popescu (Adv Math 279:104–158, 2015, Trans Am Math Soc 368:4357–4416, 2016). The purpose of this paper is to continue the line of Popescu to develop a theory of free holomorphic functions. Some results from the classical holomorphic function theory have free analogues in this noncommutative setting. In particular, we prove the maximum principle, Weierstrass and Montel type theorems for free holomorphic functions. As an application, we construct a metric on \(\mathrm{Hol}(\mathbf{B_n}(\mathcal {H}))\) such that it becomes a complete space. 相似文献
19.
单位圆盘的全纯自同构是《复变函数》课程中重要的内容之一,本文给出了单位圆盘的全纯自逆紧映照,其为单位圆盘的全纯自同构的一种推广,可供讲授《复变函数》课程的教师参考. 相似文献