ON THE SYMMETRIC *-POLYNOMIALS OF TWO COMPLEX VARIABLES
Keywords:
*-polynomial, symmetric *-polynomial.Abstract
We show that the every symmetric *-polynomial of two complex variables can be represented as an algebraic combination of the elementary symmetric *-polynomials.
References
1. Курош А.Г. Курс высшей алгебры / А.Г.Курош. – М.: Наука, 1968. – 431 с.
2. Митрофанов М.А. Аппроксимация непрерывных функций на комплексных банаховых пространствах / М.А.Митрофанов // Математичиские заметки. – 2009. – Т.86, Вип. 4. – С. 557-570.
3. Algebras of symmetric holomorphic functions on / R.Alencar, R.Aron, P.Galindo and A.Zagorodnyuk // Bull. London Math. Soc. – 2003. – V.35. – P. 55-64.
4. Chernega I. The convolution operation on the spectra of algebras of symmetric analytic functions / I.Chernega, P.Galindo and A.Zagorodnyuk // J. Math. Anal. Appl. – 2012. – V. 395. – P. 569-577.
5. Gonzales M. Symmetric polynomials on rearrangement invariant function spaces / M.Gonzales, R.Gonzalo and J.A.Jaramillo // J. London Math. Anal. Soc. – 1999. – V.59, No2. – P. 681-697.
6. Mujica J. Complex Analysis in Banach Spaces / J.Mujica // North-Holland, Amsterdam, New York, Oxford – 1986. – 447 p.
7. Nemirovskii A.S. On polynomial approximation of functions on Hilbert space / A.S.Nemirovskii, S.M.Semenov // Mat. USSR Sbornik. – 1973. – V. 21. – P. 255-277.
2. Митрофанов М.А. Аппроксимация непрерывных функций на комплексных банаховых пространствах / М.А.Митрофанов // Математичиские заметки. – 2009. – Т.86, Вип. 4. – С. 557-570.
3. Algebras of symmetric holomorphic functions on / R.Alencar, R.Aron, P.Galindo and A.Zagorodnyuk // Bull. London Math. Soc. – 2003. – V.35. – P. 55-64.
4. Chernega I. The convolution operation on the spectra of algebras of symmetric analytic functions / I.Chernega, P.Galindo and A.Zagorodnyuk // J. Math. Anal. Appl. – 2012. – V. 395. – P. 569-577.
5. Gonzales M. Symmetric polynomials on rearrangement invariant function spaces / M.Gonzales, R.Gonzalo and J.A.Jaramillo // J. London Math. Anal. Soc. – 1999. – V.59, No2. – P. 681-697.
6. Mujica J. Complex Analysis in Banach Spaces / J.Mujica // North-Holland, Amsterdam, New York, Oxford – 1986. – 447 p.
7. Nemirovskii A.S. On polynomial approximation of functions on Hilbert space / A.S.Nemirovskii, S.M.Semenov // Mat. USSR Sbornik. – 1973. – V. 21. – P. 255-277.
Downloads
Published
2019-02-16
How to Cite
Василишин, Т. В., & Струтинський, М. М. (2019). ON THE SYMMETRIC *-POLYNOMIALS OF TWO COMPLEX VARIABLES. PRECARPATHIAN BULLETIN OF THE SHEVCHENKO SCIENTIFIC SOCIETY. Number, (1(33), 88–92. Retrieved from https://pvntsh.nung.edu.ua/index.php/number/article/view/104
Issue
Section
Mathematics and Mechanics
