The theory T 0 2 , axiomatized by the induction scheme for sharply bounded formulas in Buss’ original language of bounded arithmetic (with bx/2c but not bx/2yc), has recently been unconditionally separated from full bounded arithmetic S2. The method used to prove the separation is reminiscent of those known from the study of open

Using a Riemann-Lebesgue lemma for the Fourier transform over the class of bounded variation functions that vanish at infinity, we prove the Dirichlet–Jordan theorem for functions on this class. Our proof is in the Henstock–Kurzweil integral context and is different to that of Riesz-Livingston [Amer. Math. Monthly 62 (1955), 434–437]. As consequence, we obtain the Dirichlet–Jordan theorem for f...

The present paper proposes a new condition to replace both the (O-regularly varying) quasimonotone condition and a certain type of bounded variation condition, and shows the same conclusion for the uniform convergence of certain trigonometric series still holds.

We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3]. Ÿ

For a Borel-measurable function f : R→ R satisfying f(0) = 0 and

In this paper we have introduced the notion of fuzzy real-valued p-bounded variation double sequence space p F bv 2 (1 ≤ p < ∞). We have studied some important properties like completeness, convergence free, solid, symmetric. Some inclusion results are also established.

The measure approach represents a preference relation over functions by the measure of Ž . their epigraphs or hypographs . This paper proves a measure representation theorem for a class of increasing functions and shows how its proof can be modified to yield another measure representation theorem for functions of bounded variation. q 1998 Elsevier Science B.V. JEL classification: D81

let  be a hilbert space of functions analytic on a plane domain  such that for every  in  the functional of evaluation at  is bounded. assume further that  contains the constants and admits multiplication by the independent variable , , as a bounded operator. we give sufficient conditions for  to be reflexive for all positive integers .