scholarly journals An extension theorem for holomorphic mappings - Corrigenda

1983 ◽  
Vol 94 (1) ◽  
pp. 189-189
Keyword(s):  
Tangent Space ◽  
Extension Theorem ◽  
Levi Form ◽  
Holomorphic Mappings ◽  
Additional Hypothesis ◽  
Complex Tangent

J. C. Wood. ‘An extension theorem for holomorphic mappings.’As pointed out by Y.-T. Siu [MR82d:32021] the theorems and corollary require the additional hypothesis that the boundary ∂X, is hyper-(m–1)-convex where m = dim X, i.e. for all p ∈ ∂X, the sum of the eigenvalues of the restriction of the Levi form of ∂X to the complex tangent space Tp(∂X) ∩ JTp(∂X) is non-negative.

HARTOGS-TYPE EXTENSION THEOREM AND SINGULAR SETS OF SEPARATELY HOLOMORPHIC MAPPINGS ON COMPACT SETS WITH VALUES IN A WEAKLY BRODY HYPERBOLIC COMPLEX SPACE

2001 ◽  
Vol 12 (07) ◽  
pp. 857-865
Author(s):  
DO DUC THAI ◽  
NGUYEN THI TUYET MAI
Keyword(s):  
Complex Space ◽  
Extension Theorem ◽  
Holomorphic Mappings ◽  
Compact Sets ◽  
Singular Sets ◽  
Hyperbolic Complex

We give a Hartogs-type extension theorem for separately holomorphic mappings on compact sets into a weakly Brody hyperbolic complex space. Moreover, a generalization of Saint Raymond–Siciak theorem of the singular sets of separately holomorphic mappings with values in a weakly Brody hyperbolic complex space is given.

An extension theorem for holomorphic mappings

1980 ◽  
Vol 88 (1) ◽  
pp. 125-127
Author(s):  
J. C. Wood
Keyword(s):  
Complex Structure ◽  
Extension Theorem ◽  
Holomorphic Extension ◽  
Holomorphic Mappings ◽  
Necessary Condition ◽  
Holomorphic Map ◽  
Complex Linear ◽  
Smooth Extension ◽  
Smooth Map ◽  
Topological Obstruction

Let X, Y be complex manifolds with smooth (C∞) boundaries ∂X, ∂Y. We give conditions which ensure that a smooth map Φ: ∂X → ∂Y has an extension to a holomorphic map X → Y. Let J denote the complex structure on X. We say that Φ satisfies the ‘tangential Cauchy-Riemann equation ∂¯bΦ = 0’if the differential dΦ restricted to the complex subspace Tp(∂X) ∩ JTp(∂X) of the tangent space Tp(∂X) is complex linear at all points p ∈ ∂X. Clearly this is a necessary condition for the existence of a holomorphic extension. A further necessary condition is that there exists no topological obstruction to extension, hence we assume that a smooth extension φ: X → Y is given and we shall look for a holomorphic map f: X → Y with the same boundary values.

Holomorphic Mappings between Domains in ℂ2

2012 ◽  
Vol 64 (2) ◽  
pp. 429-454
Author(s):  
Rasul Shafikov ◽  
Kaushal Verma
Keyword(s):  
Extension Theorem ◽  
Holomorphic Mappings

Abstract An extension theorem for holomorphic mappings between two domains in ℂ2is proved under purely local hypotheses.

Convergence Insufficiency Treatment Trial – Attention and Reading Trial (CITT-ART): Design and Methods

2015 ◽  
pp. 214-228 ◽  
Keyword(s):  
Clinical Trial ◽  
Randomized Clinical Trial ◽  
Health Care Providers ◽  
Developmental Disorders ◽  
Attention Problems ◽  
Secondary Outcome ◽  
Care Providers ◽  
Treatment Trial ◽  
Additional Hypothesis ◽  
Convergence Insufficiency

Objective: To describe the design and methodology of the Convergence Insufficiency Treatment Trial: Attention and Reading Trial (CITT-ART), the first randomized clinical trial evaluating the effect of vision therapy on reading and attention in school-age children with symptomatic convergence insufficiency (CI). Methods: CITT-ART is a multicenter, placebo-controlled, randomized clinical trial of 324 children ages 9 to 14 years in grades 3 to 8 with symptomatic CI. Participants are randomized to 16 weeks of office-based vergence/accommodative therapy (OBVAT) or placebo therapy (OBPT), both supplemented with home therapy. The primary outcome measure is the change in the Wechsler Individual Achievement Test-Version 3 (WIAT-III) reading comprehension subtest score. Secondary outcome measures are changes in attention as measured by the Strengths and Weaknesses of Attention (SWAN) as reported by parents and teachers, tests of binocular visual function, and other measures of reading and attention. The long-term effects of treatment are assessed 1 year after treatment completion. All analyses will test the null hypothesis of no difference in outcomes between the two treatment groups. The study is entering its second year of recruitment. The final results will contribute to a better understanding of the relationship between the treatment of symptomatic CI and its effect on reading and attention. Conclusion: The study will provide an evidence base to help parents, eye professionals, educators, and other health care providers make informed decisions as they care for children with CI and reading and attention problems. Results may also generate additional hypothesis and guide the development of other scientific investigations of the relationships between visual disorders and other developmental disorders in children.

scholarly journals Quantum Orlicz Spaces in Information Geometry

2004 ◽  
Vol 11 (04) ◽  
pp. 359-375 ◽  
Author(s):  
R. F. Streater
Keyword(s):  
Quantum Information ◽  
Tangent Space ◽  
Selfadjoint Operator ◽  
Affine Connection ◽  
Orlicz Spaces ◽  
Trace Class ◽  
Information Geometry ◽  
Young Function ◽  
Affine Structure ◽  
Cotangent Space

Let H0 be a selfadjoint operator such that Tr e−βH0 is of trace class for some β < 1, and let χɛ denote the set of ɛ-bounded forms, i.e., ∥(H0+C)−1/2−ɛX(H0+C)−1/2+ɛ∥ < C for some C > 0. Let χ := Span ∪ɛ∈(0,1/2]χɛ. Let [Formula: see text] denote the underlying set of the quantum information manifold of states of the form ρx = e−H0−X−ψx, X ∈ χ. We show that if Tr e−H0 = 1. 1. the map Φ, [Formula: see text] is a quantum Young function defined on χ 2. The Orlicz space defined by Φ is the tangent space of [Formula: see text] at ρ0; its affine structure is defined by the (+1)-connection of Amari 3. The subset of a ‘hood of ρ0, consisting of p-nearby states (those [Formula: see text] obeying C−1ρ1+p ≤ σ ≤ Cρ1 − p for some C > 1) admits a flat affine connection known as the (−1) connection, and the span of this set is part of the cotangent space of [Formula: see text] 4. These dual structures extend to the completions in the Luxemburg norms.

Sign in / Sign up

Export Citation Format

Share Document