Solutions of bounded variation of a linear homogeneous functional equation in the indeterminate case.
Solutions of bounded variation of a linear homogeneous functional equation in the indeterminate case. (Short Communication).
Solutions of Bounder Variation of a Linear Homogeneous Functional Equation
Some fine properties of sets with finite perimeter in Wiener spaces
In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...
Some results about the Henstock-Kurzweil Fourier transform
We consider the Fourier transform in the space of Henstock-Kurzweil integrable functions. We prove that the classical results related to the Riemann-Lebesgue lemma, existence and continuity are true in appropriate subspaces.
Spaces of functions of generalized bounded variation. II: Questions of uniform convergence of Fourier series.
Spectral theory and operator ergodic theory on super-reflexive Banach spaces
On reflexive spaces trigonometrically well-bounded operators have an operator-ergodic-theory characterization as the invertible operators U such that . (*) Trigonometrically well-bounded operators permeate many settings of modern analysis, and this note highlights the advances in both their spectral theory and operator ergodic theory made possible by a recent rekindling of interest in the R. C. James inequalities for super-reflexive spaces. When the James inequalities are combined with Young-Stieltjes...
Stability criteria of linear neutral systems with distributed delays
In this paper, stability of linear neutral systems with distributed delay is investigated. A bounded half circular region which includes all unstable characteristic roots, is obtained. Using the argument principle, stability criteria are derived which are necessary and sufficient conditions for asymptotic stability of the neutral systems. The stability criteria need only to evaluate the characteristic function on a straight segment on the imaginary axis and the argument on the boundary of a bounded...
Stable approximations of a minimal surface problem with variational inequalities.
Superposition operators and functions of bounded p-variation.
We characterize the set of all functions f of R to itself such that the associated superposition operator Tf: g → f º g maps the class BVp1(R) into itself. Here BVp1(R), 1 ≤ p < ∞, denotes the set of primitives of functions of bounded p-variation, endowed with a suitable norm. It turns out that such an operator is always bounded and sublinear. Also, consequences for the boundedness of superposition operators defined on Besov spaces Bp,qs are discussed.
Superpositions of transformations of bounded variation
Sur les Champs de vecteurs peu réguliers
Sur les espaces uniformément fermés de fonctions à variation bornée
Sur les fonctions non dérivables de Weierstrass
Symmetric integrals and trigonometric series [Book]
The AP-Denjoy and AP-Henstock integrals revisited
The note is related to a recently published paper J. M. Park, J. J. Oh, C.-G. Park, D. H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate basis...
The Basic Existence Theorem of Riemann-Stieltjes Integral
In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15],...
The decomposition of functions of bounded ϰ-variation into differences of ϰ-decreasing functions
The dual of the space of functions of bounded variation
In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.
The fundamental theorem of calculus for Lebesgue integral.