Search results for "First return integral"
showing 5 items of 5 documents
Derivatives not first return integrable on a fractal set
2018
We extend to s-dimensional fractal sets the notion of first return integral (Definition 5) and we prove that there are s-derivatives not s-first return integrable.
A generalized first-return integration process
2020
We extend the first-return integration process, introduced in [5] by U.B. Darji and M.J. Evans, and prove that each Lebesgue-improper integrable function f : [a, b] --> R is first-return integrable in this generalized sense to (Li)int_a^b f(t) dt.
A first return examination of vector valued integrals.
2009
We prove that for each Bochner integrable function f there exists a trajectory yielding the Bochner integral of f, and that on infinite dimensional Banach spaces there exist Pettis integrable functions f such that no trajectory yields the Pettis integral of f.
Remarks on the first return integral
2007
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.
Bollettino di Matematica pura e applicata
2020
The paper emphasizes some the advances of knowledge in mathematics problems ad new applications. The Bollettino is open to the contribution of Italian or foreign researchers.