Best Approximation with Exponential Orders and Intermediate Spaces.
Best lambda-Approximation for Entire Functions of Finite Order
Best possible sufficient conditions for the Fourier transform to satisfy the Lipschitz or Zygmund condition
We consider complex-valued functions f ∈ L¹(ℝ), and prove sufficient conditions in terms of f to ensure that the Fourier transform f̂ belongs to one of the Lipschitz classes Lip(α) and lip(α) for some 0 < α ≤ 1, or to one of the Zygmund classes zyg(α) and zyg(α) for some 0 < α ≤ 2. These sufficient conditions are best possible in the sense that they are also necessary in the case of real-valued functions f for which either xf(x) ≥ 0 or f(x) ≥ 0 almost everywhere.
Best simultaneous approximations
In this paper we study simultaneous approximation of real-valued functions in and give a generalization of some related results.
Beyond Lebesgue and Baire: generic regular variation
We show that the No Trumps combinatorial property (NT), introduced for the study of the foundations of regular variation by the authors, permits a natural extension of the definition of the class of functions of regular variation, including the measurable/Baire functions to which the classical theory restricts itself. The "generic functions of regular variation" defined here characterize the maximal class of functions to which the three fundamental theorems of regular variation (Uniform Convergence,...
Beyond Lebesgue and Baire II: Bitopology and measure-category duality
We re-examine measure-category duality by a bitopological approach, using both the Euclidean and the density topologies of the line. We give a topological result (on convergence of homeomorphisms to the identity) obtaining as a corollary results on infinitary combinatorics due to Kestelman and to Borwein and Ditor. We hence give a unified proof of the measure and category cases of the Uniform Convergence Theorem for slowly varying functions. We also extend results on very slowly varying functions...
Beyond the Gaussian.
Bi-Lipschitz Bijections of Z
It is shown that every bi-Lipschitz bijection from Z to itself is at a bounded L1 distance from either the identity or the reflection.We then comment on the group-theoretic properties of the action of bi-Lipschitz bijections.
Bi-Lipschitz embeddings of hyperspaces of compact sets
We study the bi-Lipschitz embedding problem for metric compacta hyperspaces. We observe that the compacta hyperspace K(X) of any separable, uniformly disconnected metric space X admits a bi-Lipschitz embedding in ℓ². If X is a countable compact metric space containing at most n nonisolated points, there is a Lipschitz embedding of K(X) in ; in the presence of an additional convergence condition, this embedding may be chosen to be bi-Lipschitz. By way of contrast, the hyperspace K([0,1]) of the...
Bi-Lipschitz mappings and quasinearly subharmonic functions.
Blow Up Results for Fractional Differential Equations and Systems
Bochner product integration
A new definition of the product integral is given. The definition is based on a procedure which is analogous to the sum definition of the Bochner integral given by J. Kurzweil and E.J. McShane. The new definition is shown to be equivalent to the seemingly verey different one given by J.D. Dollard and C.N. Friedman in [1] and [2].
Book Reviews
Boundary value problems for Caputo-Hadamard fractional differential inclusions in Banach spaces
In this article, we study the existence of solutions in a Banach space of boundary value problems for Caputo-Hadamard fractional differential inclusions of order .
Boundary value problems for differential equations with fractional order.
Boundary value problems for differential inclusions with fractional order
In this paper, we shall establish sufficient conditions for the existence of solutions for a boundary value problem for fractional differential inclusions. Both cases of convex valued and nonconvex valued right hand sides are considered.
Boundary value problems for Hadamard-Caputo implicit fractional differential inclusions with nonlocal conditions
In this paper, the authors establish sufficient conditions for the existence of solutions to implicit fractional differential inclusions with nonlocal conditions. Both of the cases of convex and nonconvex valued right hand sides are considered.
Boundary value problems for the Schrödinger equation involving the Henstock-Kurzweil integral
In the present paper, we investigate the existence of solutions to boundary value problems for the one-dimensional Schrödinger equation , where and are Henstock-Kurzweil integrable functions on . Results presented in this article are generalizations of the classical results for the Lebesgue integral.
Bounded linear functionals on the space of Henstock-Kurzweil integrable functions
Applying a simple integration by parts formula for the Henstock-Kurzweil integral, we obtain a simple proof of the Riesz representation theorem for the space of Henstock-Kurzweil integrable functions. Consequently, we give sufficient conditions for the existence and equality of two iterated Henstock-Kurzweil integrals.
Bounded variation and differentiability of functions.