A limit formula for regular iteration groups. (Summary).
A linear extension operator for Whitney fields on closed o-minimal sets
A continuous linear extension operator, different from Whitney’s, for -Whitney fields (p finite) on a closed o-minimal subset of is constructed. The construction is based on special geometrical properties of o-minimal sets earlier studied by K. Kurdyka with the author.
A linear functional differential equation with distributions in the input.
A linear inequality of Gronwall's type containing multiple integral
A Lipschitz function which is on a.e. line need not be generically differentiable
We construct a Lipschitz function f on X = ℝ ² such that, for each 0 ≠ v ∈ X, the function f is smooth on a.e. line parallel to v and f is Gâteaux non-differentiable at all points of X except a first category set. Consequently, the same holds if X (with dimX > 1) is an arbitrary Banach space and “a.e.” has any usual “measure sense”. This example gives an answer to a natural question concerning the author’s recent study of linearly essentially smooth functions (which generalize essentially smooth...
A local Landau type inequality for semigroup orbits
Given a strongly continuous semigroup on a Banach space X with generator A and an element f ∈ D(A²) satisfying and for all t ≥ 0 and some ω > 0, we derive a Landau type inequality for ||Af|| in terms of ||f|| and ||A²f||. This inequality improves on the usual Landau inequality that holds in the case ω = 0.
A local minimum energy condition of hexagonal circle packing.
A Loeb Measure Approach To The Riesz Representation Theorem
A logarithmic extension of the Hölder inequality.
A logarithmically completely monotonic function involving the Gamma functions.
A lower bound for ratio of power means.
A Marchaud type inequality
We present a new Marchaud type inequality in spaces.
A mean value inequality for positive integral transformations with application to a maximal theorem
A mean value property for pairs of integrals.
A measure-theoretic characterization of the Henstock-Kurzweil integral revisited
In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral.
A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions
A method for solving fuzzy Fredholm integral equations of the second kind.
A minimum energy condition of 1-dimensional periodic sphere packing.
A monotonicity criterion for arbitrary functions
A monotonicity property of power means.