Josip Globevnik
The paper gives the following characterization of the disc algebra in terms of the argument principle: A continuous function f on the unit circle T extends holomorphically through the unit disc if and only if for each polynomial P such that f+P has no zero on T the change of argument of f+P around T is nonnegative.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We construct an example of a holomorphic motion of a five-point subset of the Riemann sphere over an annulus such that it satisfies the zero winding number condition but is not fully extendable.
Let M be a finite Riemann surface and let A(bM) be the algebra of all continuous functions on bM which extend holomorphically through M. We prove that a continuous function F on bM belongs to A(bM) if for each f, g in A(bM) such that fF+g has no zero the change of argument of fF+g along bM is nonnegative.
Let D be a bounded, finitely connected domain in the complex plane without isolated points in the boundary and let f be a continuous function on the boundary bD. Let F be a continuous extension of f to the closure of D. We prove that f extends holomorphically through D if and only if the degree of F+h is nonnegative for every holomorphic function h on D such that F+h is bounded away from zero near bD.
Let D be a bounded domain in the complex plane whose boundary consists of m pairwise disjoint simple closed curves where m is greater than one. Let A(bD) be the algebra of all continuous functions on bD which extend holomorphically through D. We show that a continuous function f on bD belongs to A(bD) if for each g in A(bD) the harmonic extension of Re(fg) to D has a single valued conjugate.
Let D be a bounded domain in the complex plane whose boundary consists of finitely many pairwise disjoint simple closed curves. Give bD the standard orientation and let A(D) be the algebra of all continuous functions on the closure of D which are holomorphic on D. In the paper we prove that a continuous function f on bD extends to a function in A(D) if and only if for each g in A(D) such that f+g has no zero on bD the change of argument of f+g along bD is nonnegative.
Let B be the open unit ball in C^2 and let a, b be two points in B. It is known that for every positive integer k there is a function f in C^k(bB) which extends holomorphically into B along any complex line passing through either a or b yet f does not extend holomorphically through B. In the paper we show that there is no such function in C^\infty (bB). Moreover, we obtain a fairly complete description of pairs of points a, b in C^2 such that if a function f in C^\infty(bB) extends holomorphically into B along each complex line passing through either a or b that meets B, then f extends holomor…
Let M be a smooth generic submanifold of C^n. Tumanov showed that the direction of CR extendability parallel propagates with respect to a certain differential geometric partial connection in a quotient bundle of the normal bundle to M. M is said to be globally minimal at a point z in M if the CR orbit of z contains a neighborhood of z in M. It is shown that the vector space generated by the directions of CR-extendability of CR functions on M is preserved by the induced composed flow between two points in the same CR orbit. As an application, the main result of this paper, conjectured by J.-M. …
Since the nonlinear integral transforms $J_α[f](z) = \int_{0}^{z}(f'(u))^α du$ and $I_α[f](z) =\int_0^z (f(u)/u)^α du$ with a complex number $α$ have been introduced, a great number of studies were dedicated to deriving sufficient conditions for univalence on the unit disk. On the other hand, little is known about the conditions that $J_α[f]$ or $I_α[f]$ produces a holomorphic univalent function in the unit disk which extends to a quasiconformal map on the complex plane. In this paper we discuss quasiconformal extendibility of the integral transforms $J_α[f]$ and $I_α[f]$ for holomorphic funct…
Let U be the open unit disc in C. Given a continuous function g: bU --> C-{0} denote by W(g) the winding number of g around the origin. We prove that a continuous function f: bU --> C extends meromorphically through U if and only if there is a nonnegative integer N such that W(Pf+Q) is greater than or equal to -N for every pair P,Q of polynomials such that Pf+Q has no zero on bU. If this is the case then the meromorphic extension of f has at most N poles in U, counting multiplicity.
Let D be the open unit disc in C. The paper deals with the following conjecture: If f is a continuous function on bD such that the change of argument of Pf+1 around bD is nonnegative for every polynomial P such that Pf+1 has no zero on bD then f extends holomorphically through D. We prove a related result on meromorphic extendibility for smooth functions with finitely many zeros of finite order, which, in particular, implies that the conjecture holds for real analytic functions.
We study the holomorphic extendibility of $\text{Op}(p)u$, when $p$ is an analytic symbol, and explicit information is available on the domains of holomorphic extendibility of both $p$ and $u$. By a contour deformation argument, we obtain a precise local estimate of the domain of holomorphy of $\text{Op}(p)u$ in terms of the information on $p$ and $u$.
Let $Ω$ be a smooth real analytic submanifold of a complex manifold $X$. We establish and study the link between the following 3 subjects: 1) topological properties of smooth families of attached analytic discs, the manifold $Ω$ admits, 2) lower bounds for dimensions of complex tangent spaces of $Ω$, 3) a generalization of the argument principle for smooth families of holomorphic mappings from the standard complex disc to $X$. In particular, we obtain characterization of complex manifolds and their boundaries in terms of attached analytic discs. The special case when $Ω$ is the graph, leads to…
It is known that the Cauchy's argument principle, applied to an holomorphic function $f$, requires that $f$ has no zeros on the curve of integration. In this short note, we give a generalization of such a principle which covers the case when $f$ has zeros on the curve, as well as an application.
A version of the argument principle is established for varieties of holomorphic mappings from the unit disc to $\mathbb C^n,$ parametrized by points of real manifolds. Applications to characterization of CR functions and estimating CR dimensions of real submanifolds in $\mathbb C^n$ are given.
Kalantari's Geometric Modulus Principle describes the local behavior of the modulus of a polynomial. Specifically, if $p(z) = a_0 + \sum_{j=k}^n a_j\left(z-z_0\right)^j,\;a_0a_ka_n \neq 0$, then the complex plane near $z = z_0$ comprises $2k$ sectors of angle $\fracπ{k}$, alternating between arguments of ascent (angles $θ$ where $|p(z_0 + te^{iθ})| > |p(z_0)|$ for small $t$) and arguments of descent (where the opposite inequality holds). In this paper, we generalize the Geometric Modulus Principle to holomorphic and harmonic functions. As in Kalantari's original paper, we use these extensions …
New insights into Gleason parts for an algebra of holomorphic functions
本文研究了$\ell_p$单位球上一致连续全纯函数代数的Gleason部分结构，证明了纤维中存在大量不同的Gleason部分，并扩展了该领域的先前研究成果。
On the holomorphic differential operator $\frac{d}{dz}: Q_K\to L^q(WdA)$
该研究利用二进容量测度刻画了全纯微分算子在$Q_K$空间到$L^q(WdA)$空间上的有界性与紧性，推广了$\mathcal{Q}_p$空间的相关结果，并解决了Zhao 2009年关于复合算子的公开问题。
We utilize Cauchy's argument principle in combination with the Jacobian of a holomorphic function in several complex variables and the first moment of a ratio of two correlated complex normal random variables to prove explicit formulas for the density and the mean distribution of complex zeros of random polynomials spanned by orthogonal polynomials on the unit circle and on the unit disk. We then inquire into the consequences of their asymptotical evaluations.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。