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Displaying 181 –
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366
We shall prove the following statements: Given a sequence in a Banach space enjoying the weak Banach-Saks property, there is a subsequence (or a permutation) of the sequence such that
whenever belongs to the closed convex hull of the set of weak limit points of . In case has the Banach-Saks property and is bounded the converse assertion holds too. A characterization of reflexive spaces in terms of limit points and cores of bounded sequences is also given. The motivation for the...
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle
we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
By using the concepts of limited -converging operators between two Banach spaces and , -sets and -limited sets in Banach spaces, we obtain some characterizations of these concepts relative to some well-known geometric properties of Banach spaces, such as -Dunford–Pettis property of order and Pelczyński’s property of order , .
If the minimum problem () is the limit, in a variational sense, of a sequence of minimum problems with obstacles of the type then () can be written in the form
without any additional constraint.
Supposing that the metric space in question supports a fractional diffusion, we prove that after introducing an appropriate multiplicative factor, the Gagliardo seminorms of a function f ∈ L²(E,μ) have the property
,
where ℰ is the Dirichlet form relative to the fractional diffusion.
We collect and extend results on the limit of as σ → 0⁺ or σ → 1¯, where Ω is ℝⁿ or a smooth bounded domain, k ∈ 0,1, l ∈ ℕ, p ∈ [1,∞), and is the intrinsic seminorm of order l+σ in the Sobolev space . In general, the above limit is equal to , where c and [·] are, respectively, a constant and a seminorm that we explicitly provide. The particular case p = 2 for Ω = ℝⁿ is also examined and the results are then proved by using the Fourier transform.
We study limiting K- and J-methods for arbitrary Banach couples. They are related by duality and they extend the methods already known in the ordered case. We investigate the behaviour of compact operators and we also discuss the representation of the methods by means of the corresponding dual functional. Finally, some examples of limiting function spaces are given.
The estimate is shown to hold if and only if is elliptic and canceling. Here is a homogeneous linear differential operator of order on from a vector space to a vector space . The operator is defined to be canceling if . This result implies in particular the classical Gagliardo–Nirenberg–Sobolev inequality, the Korn–Sobolev inequality and Hodge–Sobolev estimates for differential forms due to J. Bourgain and H. Brezis. In the proof, the class of cocanceling homogeneous linear differential...
We show that if U is a domain of existence in a separable Banach space, then the set of holomorphic functions on U whose domain of existence is U is lineable and algebrable.
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