Improper Integral

Vladimir Janković

Displaying similar documents to “Improper Integral”

Henstock-Kurzweil and McShane product integration; descriptive definitions

Antonín Slavík, Štefan Schwabik (2008)

Czechoslovak Mathematical Journal

Similarity:

The Henstock-Kurzweil and McShane product integrals generalize the notion of the Riemann product integral. We study properties of the corresponding indefinite integrals (i.e. product integrals considered as functions of the upper bound of integration). It is shown that the indefinite McShane product integral of a matrix-valued function $A$ is absolutely continuous. As a consequence we obtain that the McShane product integral of $A$ over $[a, b]$ exists and is invertible if and only if $A$ is Bochner...

On the limit properties of the Picard singular integral.

Górzeńska, M., Rempulska, L. (1994)

Publications de l'Institut Mathématique. Nouvelle Série

Similarity:

Generalizations of the Riemann-Lebesgue and Cantor-Lebesgue lemmas

Charles S. Kahane (1980)

Czechoslovak Mathematical Journal

Similarity:

On a certain differential equation with time lag

Ján Ohriska (1971)

Archivum Mathematicum

Similarity:

A singular version of Leighton's comparison theorem for forced quasilinear second order differential equations

Ondřej Došlý, Jaroslav Jaroš (2003)

Archivum Mathematicum

Similarity:

We extend the classical Leighton comparison theorem to a class of quasilinear forced second order differential equations $(r (t) | x^{'} |^{α - 2} x^{'})^{'} + c (t) {| x |}^{β - 2} x = f (t), 1 < α \leq β, t \in I = (a, b), (*)$ where the endpoints $a$ , $b$ of the interval $I$ are allowed to be singular. Some applications of this statement in the oscillation theory of (*) are suggested.