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Cauchy's residue theorem for a class of real valued functions

Branko Sarić — 2010

Czechoslovak Mathematical Journal

Let $[a, b]$ be an interval in $ℝ$ and let $F$ be a real valued function defined at the endpoints of $[a, b]$ and with a certain number of discontinuities within $[a, b]$ . Assuming $F$ to be differentiable on a set $[a, b] ∖ E$ to the derivative $f$ , where $E$ is a subset of $[a, b]$ at whose points $F$ can take values $\pm \infty$ or not be defined at all, we adopt the convention that $F$ and $f$ are equal to $0$ at all points of $E$ and show that $𝒦ℋ -vt \int_{a}^{b} f = F (b) - F (a)$ , where $𝒦ℋ -vt$ denotes the total value of the integral. The paper ends with a few examples that illustrate the theory.

On totalization of the Kurzweil-Henstock integral in the multidimensional space

Branko Sarić — 2011

Czechoslovak Mathematical Journal

In this paper a full totalization is presented of the Kurzweil-Henstock integral in the multidimensional space. A residual function of the total Kurzweil-Henstock primitive is defined.

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Currently displaying 1 – 6 of 6

Cauchy's residue theorem for a class of real valued functions

On totalization of the Kurzweil-Henstock integral in the multidimensional space

On a residue of complex functions in the three-dimensional Euclidean complex vector space.

A functional expression for the curvature of hyper-dimensional Riemannian spaces.

On the finite Fourier transforms of functions with infinite discontinuities.

Conditions for convergence of the fundamental matrix of linear time-invariant time-delayed singular systems.