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Some results on uniqueness and value distribution for q-shift difference differential polynomials

Waghamore Harina P., Maligi Ramya

Fasciculi Mathematici

2020

nr 63

87--101

In this paper, we investigate the uniqueness and value distribution of g-shift difference differential polynomials of entire and meromorphic functions with zero order and obtain some results which improve and generalizes the previous results of Harina P. Waghamore and Sangeetha Anand [1].

On relative order of entire functions of several complex variables

Biswas A.

Fasciculi Mathematici

2014

Nr 52

25--34

In this paper we obtain some relationship between relative order, relative lower order, Gol’dberg order and lower Gol’dberg order of an entire functions of several complex veriables which improves some earlier results.

An Application of the Fourier Transform to Optimization of Continuous 2-D Systems

Dymkou V., Dymkov M.

International Journal of Applied Mathematics and Computer Science

2003

Vol. 13, no 1

45-54

This paper uses the theory of entire functions to study the linear quadratic optimization problem for a class of continuous 2D systems. We show that in some cases optimal control can be given by an analytical formula. A simple method is also proposed to find an approximate solution with preassigned accuracy. Some application to the 1D optimization problem is presented, too. The obtained results form a theoretical background for the design problem of optimal controllers for relevant processes.

Note on Robinson's functional equation

Piejko K.

Demonstratio Mathematica

1999

Vol. 32, nr 4

713-715

The purpose of this note is to give a new proof of the fact, that the only entire solutions of the Robinson's functional equation are given by f(z) = Az or f(z) = A sin az, where A, a are complex constants and a is real or purely imaginary.

Quadratic Optimization Problem for 2-D Linear Continuous-discrete Control Systems

Dymkov M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

1999

Vol. 47, nr 2

163-174

Linear-quadratic optimal control problem for 2-D continuous-discrete systems is considered. The developed method is based on the entire functions theory. The problem under consideration is reduced to extremal one in Hilbert space of mentioned functions. The obtained optimality conditions are expressed in terms of solutions to adjoint system. With a few optimization theory some properties of Winner-Paley space are discussed too.