Solution operators for the ...-equation on non-transversal intersections.
Solutions de l’équation et zéros de la classe de Nevanlinna dans certains domaines faiblement pseudo-convexes
Il est montré que la condition de Blaschke est nécessaire et suffisante pour qu’un sous-ensemble analytique du domaine soit l’ensemble des zéros d’une fonction de la classe de Nevanlinna.
Solutions d'un système d'équations analytiques réelles et applications
On démontre que toute solution formelle d’un système d’équations analytiques réelles (resp. polynomiales réelles) , se relève en une solution homotope à une solution analytique (resp. à une solution de Nash) aussi proche que l’on veut de pour la topologie de Krull. On utilise ce théorème pour démontrer l’algébricité (ou l’analyticité) de certains idéaux de (ou ), et aussi pour construire des déformations analytiques de germes d’ensembles analytiques en germes d’ensembles de Nash.
Solutions of the Schröder equation
Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
Solutions to -equations on strongly pseudo-convex domains with -estimates.
Solvable Lie Algebras and Generalized Cartan Matrices Arising from Isolated Singularities.
Solvable Lie algebras and the embedding of CR manifolds
In questo lavoro si dà un criterio sufficiente per l'immersione di una varietà CR astratta di codimensione arbitraria in una di codimensione CR più bassa. La condizione trovata è necessaria per l'immersione in una varietà complessa (codimensione CR uguale a zero). Essa è formulata in termini dell'esistenza di una sottoalgebra di Lie di campi di vettori complessi trasversale alla distribuzione di Cauchy-Riemann.
Solving power series equations. II. Change of ground field
We study the effect of changing the residue field, on the topological properties of local algebra homomorphisms of analytic algebras (quotients of convergent power series rings). Although injectivity is not preserved, openness and closedness in the Krull topology, simple topology, and inductive topology is preserved.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some Algebraicity Criteria for Singular Surfaces.
Some analogs of Zariski's Theorem on nodal line arrangements.
Some applications of a new integral formula for
Let M be a smooth q-concave CR submanifold of codimension k in . We solve locally the -equation on M for (0,r)-forms, 0 ≤ r ≤ q-1 or n-k-q+1 ≤ r ≤ n-k, with sharp interior estimates in Hölder spaces. We prove the optimal regularity of the -operator on (0,q)-forms in the same spaces. We also obtain estimates at top degree. We get a jump theorem for (0,r)-forms (r ≤ q-2 or r ≥ n-k-q+1) which are CR on a smooth hypersurface of M. We prove some generalizations of the Hartogs-Bochner-Henkin extension...
Some applications of Cartain's theory on three-dimensional Cauchy-Riemann geometry.
Some applications of Cauchy-Fantappie forms to (local) problems on
Some applications of functions of several complex variables to Toeplitz and subnormal operators
Some applications of geometry of Banach spaces to harmonic analysis
Some applications of the Bergman kernel to geometrical theory of functions
Some applications of the theory of harmonic integrals
In this survey, we present recent techniques on the theory of harmonic integrals to study the cohomology groups of the adjoint bundle with the multiplier ideal sheaf of singular metrics. As an application, we give an analytic version of the injectivity theorem.
Some applications of the trace condition for pluriharmonic functions in Cn.
In this paper we investigate some applications of the trace condition for pluriharmonic functions on a smooth, bounded domain in Cn. This condition, related to the normal component on ∂D of the ∂-operator, permits us to study the Neumann problem for pluriharmonic functions and the ∂-problem for (0,1)-forms on D with solutions having assigned real part on the boundary.