On The Behaviour Of Distributions At Infinity, Wiener-Tauberian Type Results
On the behaviour of Jordan-algebra norms on associative algebras
We prove that for a suitable associative (real or complex) algebra which has many nice algebraic properties, such as being simple and having minimal idempotents, a norm can be given such that the mapping (a,b) ↦ ab + ba is jointly continuous while (a,b) ↦ ab is only separately continuous. We also prove that such a pathology cannot arise for associative simple algebras with a unit. Similar results are obtained for the so-called "norm extension problem", and the relationship between these results...
On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the best constant in the Khinchin-Kahane inequality
We prove that if is the Rademacher system of functions then for any sequence of vectors in any normed linear space F.
On the Beurling algebras -derivations and extensions.
On the Beurling-Lax theorem for domains with one hole.
On the Bézout equation in the ring of periodic distributions
A corona type theorem is given for the ring D'A(Rd) of periodic distributions in Rd in terms of the sequence of Fourier coefficients of these distributions,which have at most polynomial growth. It is also shown that the Bass stable rank and the topological stable rank of D'A(Rd) are both equal to 1.
On the Bishop-Phelps-Bollobás theorem for operators and numerical radius
We study the Bishop-Phelps-Bollobás property for numerical radius (for short, BPBp-nu) of operators on ℓ₁-sums and -sums of Banach spaces. More precisely, we introduce a property of Banach spaces, which we call strongly lush. We find that if X is strongly lush and X ⊕₁ Y has the weak BPBp-nu, then (X,Y) has the Bishop-Phelps-Bollobás property (BPBp). On the other hand, if Y is strongly lush and has the weak BPBp-nu, then (X,Y) has the BPBp. Examples of strongly lush spaces are C(K) spaces, L₁(μ)...
On the Bloch space and convolution of functions in the Lp-valued case.
On the boundary of a polyhedral Banach space.
On the boundedness of classical operators on weighted Lorentz spaces.
On the boundedness of the differentiation operator between weighted spaces of holomorphic functions
We give necessary and sufficient conditions on the weights v and w such that the differentiation operator D: Hv(Ω) → Hw(Ω) between two weighted spaces of holomorphic functions is bounded and onto. Here Ω = ℂ or Ω = 𝔻. In particular we characterize all weights v such that D: Hv(Ω) → Hw(Ω) is bounded and onto where w(r) = v(r)(1-r) if Ω = 𝔻 and w = v if Ω = ℂ. This leads to a new description of normal weights.
On the boundedness of the mapping in Besov spaces
For , precise conditions on the parameters are given under which the particular superposition operator is a bounded map in the Besov space . The proofs rely on linear spline approximation theory.
On the Brudnyi-Krugljak duality theory of spaces formed by the K-method of interpolation.
On the bundle convergence of double orthogonal series in noncommutative -spaces
The notion of bundle convergence in von Neumann algebras and their -spaces for single (ordinary) sequences was introduced by Hensz, Jajte, and Paszkiewicz in 1996. Bundle convergence is stronger than almost sure convergence in von Neumann algebras. Our main result is the extension of the two-parameter Rademacher-Men’shov theorem from the classical commutative case to the noncommutative case. To our best knowledge, this is the first attempt to adopt the notion of bundle convergence to multiple series....
On the Busemann area in Minkowski spaces.
On the calculation of the Dunkl-Williams constant of normed linear spaces
Recently, Jiménez-Melado et al. [Jiménez-Melado A., Llorens-Fuster E., Mazcuñán-Navarro E.M., The Dunkl-Williams constant, convexity, smoothness and normal structure, J. Math. Anal. Appl., 2008, 342(1), 298–310] defined the Dunkl-Williams constant DW(X) of a normed linear space X. In this paper we present some characterizations of this constant. As an application, we calculate DW(ℓ2-ℓ∞) in the Day-James space ℓ2-ℓ∞.
On the canonical extensions for distributions in the space
On the Cartan-Thullen Theorem for some subalgebras of holomorphic functions in a locally convex space.
On the categories and