Search results for "Holomorphic function"
showing 10 items of 94 documents
The edge-of-the-wedge theorem for systems of constant coefficient partial differential operators. I
1988
On demontre des resultats sur l'extendabilite holomorphe des fonctions holomorphes definies sur deux coins ou plus et pour lesquelles la somme des valeurs limites s'annulent
A Note on Riesz Bases of Eigenvectors of Certain Holomorphic Operator-Functions
2001
Abstract Operator-valued functions of the form A (λ) ≔ A − λ + Q(λ) with λ ↦ Q(λ)(A − μ)− 1 compact-valued and holomorphic on certain domains Ω ⊂ C are considered in separable Hilbert space. Assuming that the resolvent of A is compact, its eigenvalues are simple and the corresponding eigenvectors form a Riesz basis for H of finite defect, it is shown that under certain growth conditions on ‖Q(λ)(A − λ)− 1‖ the eigenvectors of A corresponding to a part of its spectrum also form a Riesz basis of finite defect. Applications are given to operator-valued functions of the form A (λ) = A − λ + B(λ − D)− 1C and to spectral problems in L2(0, 1) of the form −f″(x) + p(x, λ)f′(x) + q(x, λ)f(x) = λf(x…
On certain extension theorems in the mixed Borel setting
2004
Abstract Given two sequences M 1 and M 2 of positive numbers, we give necessary and sufficient conditions under which the inclusions Λ { M 1 } ⊂ f (j) (0) j∈ N 0 : f∈ D { M 2 } [−1,1] , Λ ( M 1 ) ⊂ f (j) (0) j∈ N 0 : f∈ D ( M 2 ) [−1,1] hold, by means of explicit constructions. This answers a question raised by Chaumat and Chollet (Math. Ann. 298 (1994) 7–40). We also consider the case when [−1,1] is replaced by [−1,1]m as well as the possibility to get ultraholomorphic extensions.
Holomorphic Mappings of Bounded Type on (DF)-Spaces
1992
We study the holomorphic functions of bounded type defined on (DF)-spaces. We prove that they are of uniformly bounded type. The space of all these functions is a Frechet space with its natural topology. Some consequences and related results are obtained.
Homomorphisms and composition operators on algebras of analytic functions of bounded type
2005
Abstract Let U and V be convex and balanced open subsets of the Banach spaces X and Y, respectively. In this paper we study the following question: given two Frechet algebras of holomorphic functions of bounded type on U and V, respectively, that are algebra isomorphic, can we deduce that X and Y (or X * and Y * ) are isomorphic? We prove that if X * or Y * has the approximation property and H wu ( U ) and H wu ( V ) are topologically algebra isomorphic, then X * and Y * are isomorphic (the converse being true when U and V are the whole space). We get analogous results for H b ( U ) and H b ( V ) , giving conditions under which an algebra isomorphism between H b ( X ) and H b ( Y ) is equiv…
A Riemann manifold structure of the spectra of weighted algebras of holomorphic functions
2009
[EN] In this paper we give general conditions on a countable family V of weights on an unbounded open set U in a complex Banach space X such that the weighted space HV (U) of holomorphic functions on U has a Frechet algebra structure. For such weights it is shown that the spectrum of HV(U) has a natural analytic manifold structure when X is a symmetrically regular Banach space, and in particular when X = C-n. (C) 2009 Elsevier Ltd. All rights reserved.
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.
Behavior of holomorphic mappings on $p$-compact sets in a Banach space
2015
We study the behavior of holomorphic mappings on p-compact sets in Banach spaces. We show that the image of a p-compact set by an entire mapping is a p-compact set. Some results related to the localization of p-compact sets in the predual of homogeneous polynomials are also obtained. Finally, the "size" of p-compactness of the image of the unit ball by p-compact linear operators is studied.
Compact and Weakly Compact Homomorphisms on Fréchet Algebras of Holomorphic Functions
2002
We study homomorphisms between Frechet algebras of holomorphic functions of bounded type. In this setting we prove that any pointwise bounded homomorphism into the space of entire functions of bounded type is rank one. We characterize up to the approximation property of the underlying Banach space, the weakly compact composition operators on Hb(V), V absolutely convex open set.
Multiplicative Decompositions of Holomorphic Fredholm Functions and ψ*-Algebras
1999
In this article we construct multiplicative decompositions of holomorphic Fredholm operator valued functions on Stein manifolds with values in various algebras of differential and pseudo differential operators which are submultiplicative ψ* - algebras, a concept introduced by the first author. For Fredholm functions T(z) satisfying an obvious topological condition we. Prove (0.1) T(z) = A(z)(I + S(z)), where A(z) is holomorphic and invertible and S(z) is holomorphic with values in an “arbitrarily small” operator ideal. This is a stronger condition on S(z) than in the authors' additive decomposition theorem for meromorphic inverses of holomorphic Fredholm functions [12], where the smallness …