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Franc Forstneric - One of the best experts on this subject based on the ideXlab platform.
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Noncritical Holomorphic Functions on Stein spaces
Journal of the European Mathematical Society, 2016Co-Authors: Franc ForstnericAbstract:We prove that every reduced Stein space admits a Holomorphic Function without critical points. Furthermore, any closed discrete subset of such a space is the critical locus of a Holomorphic Function. We also show that for every complex analytic stratification with nonsingular strata on a reduced Stein space there exists a Holomorphic Function whose restriction to every stratum is noncritical. These result also provide some information on critical loci of Holomorphic Functions on desingularizations of Stein spaces. In particular, every 1-convex manifold admits a Holomorphic Function that is noncritical outside the exceptional variety.
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a complex surface admitting a strongly plurisubharmonic Function but no Holomorphic Functions
Journal of Geometric Analysis, 2015Co-Authors: Franc ForstnericAbstract:We find a domain \(X\subset \mathbb {C}\mathbb {P}^{2}\) with a strongly plurisubharmonic Function such that every Holomorphic Function on X is constant.
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a complex surface admitting a strongly plurisubharmonic Function but no Holomorphic Functions
arXiv: Complex Variables, 2012Co-Authors: Franc ForstnericAbstract:Answering an old question, we find a domain X in the complex projective plane CP^2 which admits a strongly plurisubharmonic Function, but such that every Holomorphic Function on X is constant. The domain X can be chosen diffeomorphic to an oriented real 2-plane bundle over the 2-sphere.
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Admissible boundary values of bounded Holomorphic Functions in wedges
Transactions of the American Mathematical Society, 1992Co-Authors: Franc ForstnericAbstract:If M ⊂ C N is a generic Cauchy-Riemann manifold and W ⊂ C N is a wedge domain with edge M, then every bounded Holomorphic Function on W has an admissible limit at almost every point of M. Moreover, if a Holomorphic Function f on W has a distribution boundary value (bv f) on M that is a bounded measurable Function, then f is bounded on every finer wedge near M, and its admissible limit equals (bv f)(p) at almost every point p ∈ M
C Q Ru - One of the best experts on this subject based on the ideXlab platform.
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uniform strain fields inside multiple inclusions in an elastic infinite plane under anti plane shear
Mathematics and Mechanics of Solids, 2017Co-Authors: C Q RuAbstract:This paper constructs multiple elastic inclusions with prescribed uniform internal strain fields embedded in an infinite matrix under given uniform remote anti-plane shear. The method used is based on the sufficient and necessary conditions imposed on the boundary values of a Holomorphic Function, which guarantee the existence of the Holomorphic Function in a multiply connected region. The unknown shape of each of the multiple inclusions is characterized by a polynomial conformal mapping with a finite number of unknown coefficients. With the aid of Cauchy’s integral formula and Faber series, these unknown coefficients are determined by a system of nonlinear equations. Detailed numerical examples are shown for multiple inclusions with various prescribed uniform internal strain fields, for symmetrical inclusions and for inclusions whose shapes are independent of the remote loading, respectively. It is found that the admissible range of uniform internal strain fields for multiple inclusions is moderately lar...
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uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2015Co-Authors: C Q RuAbstract:Multiple elastic inclusions with uniform internal stress fields in an infinite elastic matrix are constructed under given uniform remote in-plane loadings. The method is based on the sufficient and necessary condition imposed on the boundary value of a Holomorphic Function that guarantees the existence of the Holomorphic Function in a multiply connected region. The unknown shape of each of the multiple inclusions is characterized by a conformal mapping. This work focuses on a major large class of multiple inclusions characterized by a simple condition that covers and is much beyond the known related results reported in previous works. Extensive examples of multiple inclusions with or without geometrical symmetry are shown. Our results showed that the inclusion shapes obtained for the uniformity of internal stress fields are independent of the remote loading only when all of the multiple inclusions have the same shear modulus as that of the matrix. Moreover, specific conditions are derived on remote loading, elastic constants of the inclusions and uniform internal stress fields, which guarantee the existence of multiple symmetric inclusions or multiple rotationally symmetrical inclusions with uniform internal stress fields.
John E. Mccarthy - One of the best experts on this subject based on the ideXlab platform.
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Norm preserving extensions of bounded Holomorphic Functions
Transactions of the American Mathematical Society, 2018Co-Authors: Łukasz Kosiński, John E. MccarthyAbstract:Let $V$ be an analytic subvariety of a domain $\Omega$ in $\mathbb{C}^{n}$. When does $V$ have the property that every bounded Holomorphic Function $f$ on $V$ has an extension to a bounded Holomorphic Function on $\Omega$ with the same norm? An obvious sufficient condition is if $V$ is a Holomorphic retract of $\Omega$. We shall discuss for what domains $\Omega$ this is also necessary. This is joint work with Łukasz Kosinski.
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Pick Interpolation for free Holomorphic Functions
American Journal of Mathematics, 2015Co-Authors: Jim Agler, John E. MccarthyAbstract:We give necessary and sufficient conditions to solve an interpolation problem for free Holomorphic Functions bounded in norm on a free polynomial polyhedron. As an application, we prove that every bounded Holomorphic Function on a polynomial polyhedron extends to a bounded free Function.
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Global Holomorphic Functions in Several Noncommuting Variables
Canadian Journal of Mathematics, 2015Co-Authors: Jim Agler, John E. MccarthyAbstract:AbstractWe define a free Holomorphic Function to be a Function that is locally, with respect to the free topology, a bounded nc-Function. We prove that free Holomorphic Functions are the Functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic Functions.
Nina Zorboska - One of the best experts on this subject based on the ideXlab platform.
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intrinsic operators from Holomorphic Function spaces to growth spaces
Integral Equations and Operator Theory, 2017Co-Authors: Nina ZorboskaAbstract:We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of Holomorphic Functions into a particular type of spaces of Functions determined by the growth of the Functions, or the growth of the Functions derivatives. The results show that the boundedness and compactness of such intrinsic operators depends only on the behaviour on the kernel Functions. They also generalize previous similar results about several specific classes of operators, such as the multiplication, composition and integral operators.
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intrinsic operators from Holomorphic Function spaces to growth spaces
arXiv: Functional Analysis, 2017Co-Authors: Nina ZorboskaAbstract:We determine the boundedness and compactness of a large class of operators, mapping from general Banach spaces of Holomorphic Functions into a particular type of spaces of Functions determined by the growth of the Functions, or the growth of the Functions derivatives. The results show that the boundedness and compactness of such intrinsic operators depends only on the behaviour on the point evaluation Functionals. They also generalize previous similar results about several specific classes of operators, such as the multiplication, composition and integral operators.
Monguzzi Alessandro - One of the best experts on this subject based on the ideXlab platform.
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Holomorphic Function spaces on the Hartogs triangle
2020Co-Authors: Monguzzi AlessandroAbstract:The definition of classical Holomorphic Function spaces such as the Hardy space or the Dirichlet space on the Hartogs triangle is not canonical. In this paper we introduce a natural family of Holomorphic Function spaces on the Hartogs triangle which includes some weighted Bergman spaces, a candidate Hardy space and a candidate Dirichlet space. For the weighted Bergman spaces and the Hardy space we study the $L^p$ mapping properties of Bergman and Szeg\H{o} projection respectively, whereas for the Dirichlet space we prove it is isometric to the Dirichlet space on the bidisc.Comment: Some arguments has been shortened. Added some comments and references. Corrected some typo