Weak compactness of integration maps associated with indefinite integrals of spectral measures

Weak Compactness of the Set of ε-Extensions

On indefinite BV-integrals

In 1986 Bruckner, Fleissner and Foran [2] obtained a descriptive definition of a minimal extension of the Lebesgue integral which integrates the derivative of any differentiable function. Recently, Bongiorno, Di Piazza and Preiss [1] showed that this minimal integral can be obtained from McShane’s definition of the Lebesgue integral [4] by imposing a mild regularity condition on McShane’s parti...

Relative Compactness and Product Stable Quotient Maps

A Note on Indefinite Integrals

1. G. H. Hardy and M. Riesz, The general theory of Dirichlet's series, London, 1915. 2. E. Kogbetliantz, Sur la sommation des séries divergentes par les moyennes simples et doubles, Ann. École Norm. (3) vol. 42 (1925) pp. 193-216. 3. Otto Szász, Verallgemeinerung eines Littlewood'sehen Salzes über Potenzreihen, J. London Math. Soc. vol. 3 (1928) pp. 254-262. 4. A. Zygmund, Remarque sur la somma...

Numerical indefinite integration of functions with singularities

We derive an indefinite quadrature formula, based on a theorem of Ganelius, for Hp functions, for p > 1, over the interval (−1, 1). The main factor in the error of our indefinite quadrature formula is O(e−π √ ), with 2N nodes and 1 p + 1 q = 1. The convergence rate of our formula is better than that of the Stenger-type formulas by a factor of √ 2 in the constant of the exponential. We conjectur...