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Displaying 41 –
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1284
Let be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in , Sobolev, and some new Hardy spaces naturally associated to .
First, we show that the...
The structure of the section space of a real analytic vector bundle on a real analytic manifold X is studied. This is used to improve a result of Grothendieck and Poly on the zero spaces of elliptic operators and to extend a result of Domański and the author on the non-existence of bases to the present case.
We say that a collection of subsets of has property if there is a set and point-countable collections of closed subsets of such that for any there is a finite subcollection of such that . Then we prove that any compact space is Corson if and only if it has a point-- base. A characterization of Corson compacta in terms of (strong) point network is also given. This provides an answer to an open question in “A Biased View of Topology as a Tool in Functional Analysis” (2014) by...
We study three closely related concepts in the context of the Banach algebra C₀(X,A). We show that, to a certain extent, Segal extensions, norm irregularity and the existence of approximate identities in C₀(X,A) can be deduced from the corresponding features of A and vice versa. Extensive use is made of the multiplier norm and the tensor product representation of C₀(X,A).
In this paper we make use of a new concept of φ-stability for Banach spaces, where φ is a function. If a Banach space X and the function φ satisfy some natural conditions, then X is saturated with subspaces that are φ-stable (cf. Lemma 2.1 and Corollary 7.8). In a φ-stable Banach space one can easily construct basic sequences which have a property P(φ) defined in terms of φ (cf. Theorem 4.5).
This leads us, for appropriate functions φ, to new results on the existence of unconditional...
We characterize the AR property in convex subsets of metric linear spaces in terms of certain near-selections.
We prove that the initial value problem for the semi-linear Schrödinger and wave equations is well-posed in the Besov space , when the nonlinearity is of type , for . This allows us to obtain self-similar solutions, as well as to recover previously known results for the solutions under weaker smallness assumptions on the data.
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