Boundary Morera theorems for holomorphic functions of several complex variables

DOI10.1215/S0012-7094-91-06428-8zbMath0760.32002OpenAlexW1568792059MaRDI QIDQ1190832

Josip Globevnik, Edgar Lee Stout

Publication date: 27 September 1992

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-91-06428-8

zbMATH Keywords

holomorphic functionsMorera propertyextension from the boundary

Mathematics Subject Classification ID

Continuation of analytic objects in several complex variables (32D15) (overlinepartial) and (overlinepartial)-Neumann operators (32W05) Boundary behavior of holomorphic functions of several complex variables (32A40) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25) Holomorphic functions of several complex variables (32A10)

Related Items

HARTOGS' SEPARATE ANALYTICITY THEOREM FOR CR FUNCTIONS ⋮ Morera conditions along real planes and a characterization of CR functions on boundaries of domains in \(\mathbb{C}^ N\) ⋮ Holomorphic Extension of Continuous Functions Along Finite Families of Complex Lines in a Ball ⋮ The boundary Morera theorem for domain $\tau^+(n-1)$ ⋮ On holomorphy of functions representable by the logarithmic residue formula ⋮ On the Multidimensional Boundary Analogue of the Morera Theorem ⋮ Holomorphic extension of functions along finite families of complex straight lines in an \(n\)-circular domain ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Propagation of boundary CR foliations and Morera type theorems for manifolds with attached analytic discs ⋮ On a certain boundary analog of Morera's theorem ⋮ Testing families of complex lines for the unit ball ⋮ Some problems of complex analysis in matrix Siegel domains ⋮ A Morera theorem for the boundary values of holomorphic functions in the unit ball in \(\mathbb C^ N\). ⋮ Some families of complex lines sufficient for holomorphic extension of functions ⋮ Parametric argument principle and its applications to CR functions and manifolds ⋮ On family of complex straight lines sufficient for existence of holomorphic continuation of continuous functions on boundary of domain ⋮ Holomorphic extension from the sphere to the ball ⋮ Extremal discs and holomorphic extension from convex hypersurfaces ⋮ A boundary Morera theorem ⋮ Analog of a theorem of Forelli for boundary values of holomorphic functions on the unit ball of \(\mathbb C^n\) ⋮ Minimal dimension families of complex lines sufficient for holomorphic extension of functions ⋮ An analog of the Hartogs theorem in a ball of ⋮ CR foliations, the strip-problem and Globevnik-Stout conjecture ⋮ On families of complex lines sufficient for holomorphic extension ⋮ A conjecture of Globevnik-Stout and a theorem of Morera for a holomorphic chain ⋮ Sur la caractérisation du bord d'une chaîne holomorphe dans l'espace projectif ⋮ Multidimensional Boundary Analog of the Hartogs Theorem in Circular Domains ⋮ Functions with the One-dimensional Holomorphic Extension Property ⋮ On a boundary Morera theorem for classical domains

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Boundary analogues of Hartog's theorem
• Holomorphic extension from spheres in \({\mathbb{C}}^ n\)
• A theorem on holomorphic extension of CR-functions
• On images of Radon transforms
• The Radon transform
• A support theorem for the \(X\)-ray transform
• Andreotti-Grauert theory by integral formulas. (Licensed ed. of the Akademie Verlag, Berlin)
• Moebius-invariant function spaces on balls and spheres
• Boundary properties of holomorphic functions of several complex variables
• A Boundary Analogue of Morera's Theorem in the Unit Ball of C n
• Rado's Theorem for CR-Functions
• On Boundary Values of Holomorphic Functions on Balls
• Analytic continuation and boundary continuity of functions of several complex variables
• On holomorphic extensions from spheres in ℂ²
• Uniform asymptotic expansions at a caustic
• A Generalization of a Theorem of Hans Lewy
• The boundary values of holomorphic functions of several complex variables