Search results for "Mathematics::Complex Variables"
showing 10 items of 96 documents
Quasianalytic Denjoy-Carleman classes and o-minimality
2003
We show that the expansion of the real field generated by the functions of a quasianalytic Denjoy-Carleman class is model complete and o-minimal, provided that the class satisfies certain closure conditions. Some of these structures do not admit analytic cell decomposition, and they show that there is no largest o-minimal expansion of the real field.
Convex functions on Carnot Groups
2007
We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
New isoperimetric estimates for solutions to Monge - Ampère equations
2009
Abstract We prove some sharp estimates for solutions to Dirichlet problems relative to Monge–Ampere equations. Among them we show that the eigenvalue of the Dirichlet problem, when computed on convex domains with fixed measure, is maximal on ellipsoids. This result falls in the class of affine isoperimetric inequalities and shows that the eigenvalue of the Monge–Ampere operator behaves just the contrary of the first eigenvalue of the Laplace operator.
The branch set of a quasiregular mapping between metric manifolds
2016
Abstract In this note, we announce some new results on quantitative countable porosity of the branch set of a quasiregular mapping in very general metric spaces. As applications, we solve a recent conjecture of Fassler et al., an open problem of Heinonen–Rickman, and an open question of Heinonen–Semmes.
Sobolev classes of Banach space-valued functions and quasiconformal mappings
2001
We give a definition for the class of Sobolev functions from a metric measure space into a Banach space. We give various characterizations of Sobolev classes and study the absolute continuity in measure of Sobolev mappings in the “borderline case”. We show under rather weak assumptions on the source space that quasisymmetric homeomorphisms belong to a Sobolev space of borderline degree; in particular, they are absolutely continuous. This leads to an analytic characterization of quasiconformal mappings between Ahlfors regular Loewner spaces akin to the classical Euclidean situation. As a consequence, we deduce that quasisymmetric maps respect the Cheeger differentials of Lipschitz functions …
Tangency conditions for multivalued mappings
1996
We prove that interiority conditions imply tangency conditions for two multivalued mappings from a topological space into a normed vector space. As a consequence, we obtain the lower semicontinuity of the intersection of two multivalued mappings. An application to the epi-upper semicontinuity of the sum of convex vector-valued mappings is given.
Entire Functions of Bounded Type on Fréchet Spaces
1993
We show that holomorphic mappings of bounded type defined on Frechet spaces extend to the bidual. The relationship between holomorphic mappings of bounded type and of uniformly bounded type is discussed and some algebraic and topological properties of the space of all entire mappings of (uniformly) bounded type are proved, for example a holomorphic version of Schauder's theorem.
A space of projections on the Bergman space
2010
We define a set of projections on the Bergman space A 2 , which is parameterized by an ane subset of a Banach space of holomorphic functions in the disk and which includes the classical Forelli-Rudin projections.
Weakly uniformly continuous holomorphic functions and the approximation property
2001
Abstract We study the approximation property for spaces of Frechet and Gâteaux holomorphic functions which are weakly uniformly continuous on bounded sets. We show when U is a balanced open subset of a Baire or barrelled metrizable locally convex space, E , that the space of holomorphic functions which are weakly uniformly continuous on U -bounded sets has the approximation property if and only if the strong dual of E , E ′ b , has the approximation property. We also characterise the approximation property for these spaces of vector-valued holomorphic functions in terms of the tensor product of the corresponding space of scalar-valued holomorphic functions and the range space.
Holomorphically ultrabornological spaces and holomorphic inductive limits
1987
Abstract The holomorphically ultrabornological spaces are introduced. Their relation with other holomorphically significant classes of locally convex spaces is established and separating examples are given. Some apparently new properties of holomorphically barrelled spaces are included and holomorphically ultrabornological spaces are utilized in a problem posed by Nachbin.