Fejér Polynomials and Control of Nonlinear Discrete Systems

Dmitrishin, Dmitriy; Hagelstein, Paul; Khamitova, Anna; Korenovskyi, Anatolii A.; Stokolos, Alexander M.

doi:10.1007/s00365-019-09472-3

Cited by 11 publications

(6 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where F N (z) is any polynomial of degree N with zero coe cient zero. e solution to this extreme problem as well very elegant and surprising applications to discrete dynamic systems are given in [8].…”

Section: E Smentioning

confidence: 99%

On Suffridge polynomials

Dillies,

Dmitrishin,

Stokolos

2020

Preprint

View full text Add to dashboard Cite

show abstract

Section: E Smentioning

confidence: 99%

On Suffridge polynomials

Dillies,

Dmitrishin,

Stokolos

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Note that changing the schlicht normalization F (0) = 0, F ′ (0) = 1 to the normalization F (0) = 0, F (1) = 1 leads to other extremal polynomials, namely, to the Suffridge and odd Fejér polynomials, which is interesting in itself. Details can be found in [10].…”

Section: Resultsmentioning

confidence: 99%

An extremal problem for polynomials

Dmitrishin

Smorodin

Stokolos

2022

Applied and Computational Harmonic Analysis

View full text Add to dashboard Cite

“…Finally, let us note that some extremal typically real polynomials can be used in the problems of stability in discrete dynamical systems [5].…”

Section: Solution Of the Main Problemmentioning

confidence: 99%

On C. Michel's hypothesis about the modulus of typically real polynomials

Dmitrishin¹,

Smorodin²,

Stokolos³

2020

Preprint

View full text Add to dashboard Cite

Extremal problems for typically real polynomials go back to a paper by W. W. Rogosinski and G. Szegő, where a number of problems were posed, which were partially solved by using orthogonal polynomials. Since then, not too many new results on extremal properties of typically real polynomials have been obtained. Fundamental work in this direction is due to M. Brandt, who found a novel way of solving extremal problems. In particular, he solved C. Michel's problem of estimating the modulus of a typically real polynomial of odd degree. On the other hand, D. K. Dimitrov showed the effectivity of Fejér's method for solving the Rogosinski-Szegő problems. In this article, we completely solve Michel's problem by using Fejér's method.N +2 2 , but its uniqueness was not considered.

show abstract

Fejér Polynomials and Control of Nonlinear Discrete Systems

Abstract: We consider optimization problems associated to a delayed feedback control (DFC) mechanism for stabilizing cycles of one dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing T

Cited by 11 publications

References 14 publications

On Suffridge polynomials

On Suffridge polynomials

An extremal problem for polynomials

On C. Michel's hypothesis about the modulus of typically real polynomials

Contact Info

Product

Resources

About