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.
Cauchy's residue theorem for a class of real valued functions
Let be an interval in and let be a real valued function defined at the endpoints of and with a certain number of discontinuities within . Assuming to be differentiable on a set to the derivative , where is a subset of at whose points can take values or not be defined at all, we adopt the convention that and are equal to at all points of and show that , where 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
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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