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1
Content available remote On the generalized growth and approximation of entire solutions of certain elliptic partial differential equation
Kumar Devendra, Alghamdi Azza M.
Demonstratio Mathematica
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2022
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Vol. 55, nr 1
429--436
EN
For an entire function solution of generalized bi-axisymmetric potential equation, we obtain a relationship between the generalized growth characteristics and polynomial approximation errors in sup norm by using the general functions introduced by Seremeta [On the connection between the growth of the maximum modulus of an entire function and the moduli of the coefficients of its power series expansion, Amer. Math. Soc. Transl. 88 (1970), no. 2, 291–301].
2
Content available Fast growing solutions to linear differential equations with entire coefficients having the same ρϕ-order
Belaϊdi Benharrat
Journal of Mathematics and Applications
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2019
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Vol. 42
63--77
EN
This paper deals with the growth of solutions of a class of higher order linear differential equations f(k)+Ak-1(z)f(k-1)+ … +A1(z)f’+A0(z)f=0; k≥2 when most coefficients Aj (z) (j = 0, ..., k-1) have the same ρϕ-order with each other. By using the concept of τϕ-type, we obtain some results which indicate growth estimate of every non-trivial entire solution of the above equations by the growth estimate of the coefficient A0 (z). We improve and generalize some recent results due to Chyzhykov-Semochko and the author.
3
Content available remote Analytic functions in the unit ball of bounded L-index in joint variables and of bounded L-index in direction: a connection between these classes
Bandura Andriy, Skaskiv Oleh
Demonstratio Mathematica
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2019
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Vol. 52, nr 1
82--87
EN
We give negative answer to the question of Bordulyak and Sheremeta for more general classes of entire functions than in the original formulation: Does index boundedness in joint variables for an entire function F imply index boundedness in the variable zj for the function F? This question is addressed for entire functions of bounded L-index in joint variables and entire functions of bounded L-index in direction. We also present a class of analytic functions in the unit ball which has bounded L-index in joint variablesand has unbounded l-index in the variables z1 and z2 for any positive continuous function l : B2→C.
4
Content available Properties of entire solutions of some linear PDE's
Bandura A, Skaskiv O., Filevych P.
Journal of Applied Mathematics and Computational Mechanics
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2017
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Vol. 16, nr 2
17--28
EN
In this paper, there are improved sufficient conditions of boundedness of the L-index in a direction for entire solutions of some linear partial differential equations. They are new even for the one-dimensional case and L≡1. Also, we found a positive continuous function l such that entire solutions of the homogeneous linear differential equation with arbitrary fast growth have a bounded l -index and estimated its growth.
5
Content available remote On the generalized order and generalized type of entire monogenic functions
Srivastava G. S., Kumar S.
Demonstratio Mathematica
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2013
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Vol. 46, nr 4
663--677
EN
In the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.
6
Approximation of entire function solutions of the Helmholtz equation having slow growth
Kumar D.
Journal of Applied Analysis
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2012
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Vol. 18, nr 2
179-196
EN
In this paper, we study the Chebyshev polynomial approximation of entire solutions of Helmholtz equations in R2 in Banach spaces (B(p, q, m) space, Hardy space and Bergman space). Some bounds on generalized order of entire solutions of Helmholtz equations of slow growth have been obtained in terms of the coefficients and approximation errors using function theoretic methods.
7
Content available remote Spaces of entire functions represented by vector valued Dirichlet series
Srivastava G. S., Sharma A.
Journal of Mathematics and Applications
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2011
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Vol. 34
97--107
EN
Spaces of entire functions ƒ represented by vector valued Dirichlet series and having finite order and finite type are considered. These are endowed with a certain topology under which they become a Frechet space. On this space the form of linear continuous functionals is characterized. Proper bases are also characterized in terms of growth parameters.
8
Content available remote 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
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2003
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Vol. 13, no 1
45-54
EN
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.
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