Frigyes Riesz [nekrolog]
Dynamické systémy s regulární pravou stranou. II
Dynamické systémy s regulární pravou stranou. I
Integral representation of -variable positive real functions
The multidimensional -transform and its use in solution of partial difference equations
On the decomposition of a positive real function into positive real summands
Analytic functions of one variable with positive real part in the right half-plane, assuming real values on the real positive half-axis, are called positive real functions. In the paper necessary and sufficient conditions for a positive real function to be a sum of two positive real functions are given. Further the structure of any positive real function is shown when written in the form where are positive real functions and has all the pure imaginary poles of the function .
O aproximací obrazu v Hilbertově transformací ortogonálními řadami racionálních lomených funkcí
On quadratic Hurwitz forms. I
Homogeneous quadratic polynomials in complex variables are investigated and various necessary and sufficient conditions are given for to be nonzero in the set . Conclusions for the theory of multivariable positive real functions are formulated with applications in multivariable electrical network theory.
Zur geometrischen Bedeutung der Gruppen der automorphen Kollineationen einer harmonischen und äquianharmonischen kubischen Kurve
On generalized difference equations
In this paper linear difference equations with several independent variables are considered, whose solutions are functions defined on sets of -dimensional vectors with integer coordinates. These equations could be called partial difference equations. Existence and uniqueness theorems for these equations are formulated and proved, and interconnections of such results with the theory of linear multidimensional digital systems are investigated. Numerous examples show essential differences of the results...
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