A multi-dimensional spectral theory in C*-algebras
A natural localization of Hardy spaces in several complex variables
Let H²(bΩ) be the Hardy space of a bounded weakly pseudoconvex domain in . The natural resolution of this space, provided by the tangential Cauchy-Riemann complex, is used to show that H²(bΩ) has the important localization property known as Bishop’s property (β). The paper is accompanied by some applications, previously known only for Bergman spaces.
A new invariant Kähler metric on relatively compact domains in a complex manifold
We introduce a new invariant Kähler metric on relatively compact domains in a complex manifold, which is the Bergman metric of the L² space of holomorphic sections of the pluricanonical bundle equipped with the Hermitian metric introduced by Narasimhan-Simha.
A New Proof of the Newlander-Nirenberg Theorem.
A note on Alexander's theorem.
A note on Banach algebras that are not isomorphic to a group algebra.
A note on geometric means of entire functions of two complex variables
A note on matrix transformations of holomorphic Dirichlet series.
A note on the Cauchy-Bochner formula for a class of Beurling ultradistributions
A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for the ∂̅-operator
We give upper and lower bounds for constants appearing in the L²-estimates for the ∂̅-operator due to Donnelly-Fefferman and Berndtsson.
A note on the Nullstellensatz for c-holomorphic functions
We begin this article with a graph theorem and a kind of Nullstellensatz for weakly holomorphic functions. This yields a general Nullstellensatz for c-holomorphic functions on locally irreducible sets. In Section 2 some methods of Płoski-Tworzewski permit us to prove an effective Nullstellensatz for c-holomorphic functions in the case of a proper intersection with the degree of the intersection cycle as exponent. We also extend this result to the case of isolated improper intersection, generalizing...
A notion of boundedness for hyperfunctions and Massera type theorems
For some classes of periodic linear ordinary differential equations and functional equations, it is known that the existence of a bounded solution in the future implies the existence of a periodic solution. In order to think on such phenomena for hyperfunction solutions to linear functional equations, we introduced a notion of bounded hyperfunctions, and translated the problems into the problems on analytic solutions to some equations in complex domains. In this article, after...
A notion of extremal analytic discs related to interpolation in the ball.
A Peak Set of Hausdorff Dimension 2n? 1 for the Algebra A(D) in the Boundary of a Domain D with C°°-Boundary in Cn.
A pointwise growth estimate for analytic functions in tubes.
A Precise Result on the Boundary Regularity of Biholomorphic Mappings.
A property of determining sets for analytic functions
A Pseudo-convex Domain not Admitting a Holomorphic Support Function.
A pure smoothness condition for Radó’s theorem for -analytic functions
Let be a bounded, simply connected -convex domain. Let and let be a function on which is separately -smooth with respect to (by which we mean jointly -smooth with respect to , ). If is -analytic on , then is -analytic on . The result is well-known for the case , , even when a priori is only known to be continuous.
A Realization Problem in the Theory of Analytic curves