23 research outputs found
Un nuovo integrale per il problema delle primitive
We introduce a new type of integral, which solves the problem of finding antiderivatives but which does not contain the improper integral
Integrals and Banach spaces for finite order distributions
summary:Let denote the real-valued functions continuous on the extended real line and vanishing at . Let denote the functions that are left continuous, have a right limit at each point and vanish at . Define to be the space of tempered distributions that are the th distributional derivative of a unique function in . Similarly with from . A type of integral is defined on distributions in and . The multipliers are iterated integrals of functions of bounded variation. For each , the spaces and are Banach spaces, Banach lattices and Banach algebras isometrically isomorphic to and , respectively. Under the ordering in this lattice, if a distribution is integrable then its absolute value is integrable. The dual space is isometrically isomorphic to the functions of bounded variation. The space is the completion of the functions in the Alexiewicz norm. The space contains all finite signed Borel measures. Many of the usual properties of integrals hold: Hölder inequality, second mean value theorem, continuity in norm, linear change of variables, a convergence theorem
Remarks on the first return integral
Some pathological properties of the first-return integrals are explored.
In particular it is proved that there exist Riemann improper
integrable functions which are first-return recoverable almost
everywhere, but not first-return integrable, with respect to each
trajectory. It is also proved that the usual convergence theorems
fail to be true for the first-return integrals
On the first return integrals
Some pathological properties of the first-return integrals are explored. In particular it is proved that there
exist Riemann improper integrable functions which are first-return recoverable almost everywhere, but not
first-return integrable, with respect to each trajectory. It is also proved that the usual convergence theorems
fail to be true for the first-return integrals
Giovanni Battista Guccia: pioneer of international cooperation in mathematics
This book examines the life and work of mathematician Giovanni Battista Guccia, founder of the Circolo Matematico di Palermo and its renowned journal, the Rendiconti del Circolo matematico di Palermo. The authors describe how Guccia, an Italian geometer, was able to establish a mathematical society in Sicily in the late nineteenth century, which by 1914 would grow to become the largest and most international in the world, with one of the most influential journals of the time. The book highlights the challenges faced by Guccia in creating an international society in isolated Palermo, and places Guccia’s activities in the wider European context through comparisons with the formation of the London Mathematical Society and the creation of Mittag-Leffler’s Acta Mathematica in Stockholm. Based on extensive searches in European archives, this scholarly work follows both historical and scientific treads, and will appeal to those interested in the history of mathematics and science in general
Multipliers for generalized Riemann integrals in the real line
summary:We use an elementary method to prove that each function is a multiplier for the -integral