Homogenization of -laplacian in perforated domain
Homogenization of periodic nonconvex integral functionals in terms of Young measures
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the -limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
Homogenization of periodic nonconvex integral functionals in terms of Young measures
Homogenization of periodic functionals, whose integrands possess possibly multi-well structure, is treated in terms of Young measures. More precisely, we characterize the Γ-limit of sequences of such functionals in the set of Young measures, extending the relaxation theorem of Kinderlherer and Pedregal. We also make precise the relationship between our homogenized density and the classical one.
Homogenous Banach spaces on the unit circle.
We prove that a homogeneous Banach space B on the unit circle T can be embedded as a closed subspace of a dual space Ξ*B contained in the space of bounded Borel measures on T in such a way that the map B → Ξ*B defines a bijective correspondence between the class of homogeneous Banach spaces on T and the class of prehomogeneous Banach spaces on T.We apply our results to show that the algebra of all continuous functions on T is the only homogeneous Banach algebra on T in which every closed ideal has...
Homomorphisms between algebras of holomorphic functions in infinite dimensional spaces
It is shown that a homomorphism between certain topological algebras of holomorphic functions is continuous if and only if it is a composition operator.
Homomorphisms on C...(E) and C...-bounding Sets.
Homomorphisms on some Function Algebras.
Hopf algebras of smooth functions on compact Lie groups
A -Hopf algebra is a -algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those -Hopf algebras which are given by the algebra of smooth functions on some compact Lie group , thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.
How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?
For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur...
How far is C(ω) from the other C(K) spaces?
Let us denote by C(α) the classical Banach space C(K) when K is the interval of ordinals [1,α] endowed with the order topology. In the present paper, we give an answer to a 1960 Bessaga and Pełczyński question by providing tight bounds for the Banach-Mazur distance between C(ω) and any other C(K) space which is isomorphic to it. More precisely, we obtain lower bounds L(n,k) and upper bounds U(n,k) on d(C(ω),C(ωⁿk)) such that U(n,k) - L(n,k) < 2 for all 1 ≤ n, k < ω.
How smooth is almost every function in a Sobolev space?
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
How the μ-deformed Segal-Bargmann space gets two measures
This note explains how the two measures used to define the μ-deformed Segal-Bargmann space are natural and essentially unique structures. As is well known, the density with respect to Lebesgue measure of each of these measures involves a Macdonald function. Our primary result is that these densities are the solution of a system of ordinary differential equations which is naturally associated with this theory. We then solve this system and find the known densities as well as a "spurious" solution...
How to define reasonably weighted Sobolev spaces
How to get rid of one of the weights in a two-weight Poincaré inequality?
We prove that if a Poincaré inequality with two different weights holds on every ball, then a Poincaré inequality with the same weight on both sides holds as well.
How to Obtain Vector-Valued Banach-Stone Theorems by Using M-Structure Methods.
Hp (Rn) is equidistributed with Lp (Rn).
Hyperbolic equations and irregularity
Hyperbolic evolution semigroups on vector valued function spaces.
Hypercyclic convolution operators on entire functions of Hilbert-Schmidt holomorphy type
Hyperinvariant subspaces of the harmonic Dirichlet space.