References
-
Alencar R., Aron R., Galindo P., Zagorodnyuk A.
Algebra of symmetric holomorphic functions on $\ell_p$.
Bull. Lond. Math. Soc. 2003, 35, 55-64.
doi: 10.1112/S0024609302001431
-
Aron R., Falcó J., Maestre M.
Separation theorems for group invariant polynomials.
J. Geom. Anal. 2018, 28 (1), 393-404.
doi: 10.1007/s12220-017-9825-0.
-
Aron R., Galindo P., Pinasco D., Zalduendo I.
Group-symmetric holomorphic functions on a Banach space.
Bull. Lond. Math. Soc. 2016, 48 (5), 779-796.
doi: 10.1112/blms/bdw043
-
Chernega I., Holubchak O., Novosad Z., Zagorodnyuk A.
Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces.
European Journal of Mathematics 2020, 6, 153-163.
doi: 10.1007/s40879-019-00390-z
-
Chernega I., Galindo P., Zagorodnyuk A.
Some algebra of symmetric analytic functions and their spectra.
Proc. Edinburgh Math. Soc. 2012, 55, 125-142.
doi: 10.1017/S0013091509001655
-
Chernega I., Galindo P., Zagorodnyuk A.
The convolution operation on the spectra of algebras of symmetric analytic functions.
J. Math. Anal. Appl. 2012, 395 (2), 569-577.
doi: 10.1016/j.jmaa.2012.04.087
-
Chernega I., Zagorodnyuk A.
Note on bases in algebras of analytic functions on Banach spaces.
Carpathian Math. Publ. 2019, 11 (1), 42-47.
doi: 10.15330/cmp.11.1.42-47
-
Galindo P., Vasylyshyn T., Zagorodnyuk A.
Symmetric and finitely symmetric polynomials on the spaces $\ell_{\infty}$ and $L_{\infty} [0, + \infty]$.
Math. Nachr. 2018, 291 (11-12), 1712-1726.
doi: 10.1002/mana.201700314
-
Galindo P., Vasylyshyn T., Zagorodnyuk A.
Analytic structure on the spectrum of the algebra of symmetric analytic functions on $L_\infty$.
RACSAM 2020, 114 (56), 13 pages.
doi: 10.1007/s13398-020-00791-w
-
Gonzalez M., Gonzalo R., Jaramillo J.
Symmetric polynomials on rearrangement invariant function spaces.
J. Lond. Math. Soc. 1999, 59 (2), 681-697.
doi: 10.1112/S0024610799007164
-
Halushchak S.
Spectra of some algebras of entire functions of bounded type, generated by a sequence of polynomials.
Carpathian Math. Publ. 2019, 11 (2), 311-320.
doi: 10.15330/cmp.11.2.311-320
-
Jawad F., Zagorodnyuk F.
Supersymmetric Polynomials on the Space of Absolutely Convergent Series.
Symmetry 2019, 11 (9), 1111.
doi: 10.3390/sym11091111
-
Kravtsiv V.
The Analogue of Newton’s Formula for Block-Symmetric Polynomials.
International Journal of Mathematical Analysis 2016, 10 (7), 323-327.
doi: 10.12988/ijma.2016.617
-
Kravtsiv V., Vasylyshyn T., Zagorodnyuk A.
On Algebraic Basis of the Algebra of Symmetric Polynomials on $l_p(C^n)$.
J. Funct. Spaces 2017, 2017, Article ID 4947925, 8 pages.
doi: 10.1155/2017/4947925
-
Kravtsiv V.V., Zagorodnyuk A.V.
Multiplicative Convolution on the Algebra of Block-Semmetric Analytic Functions.
J. Math. Sci. (N.Y.) 2020, 246 (2), 245-255.
doi: 10.1007/s10958-020-04734-z
-
Kravtsiv V.V., Zagorodnyuk A.V.
On algebraic bases of algebras of block-symmetric polynomials on Banach spaces.
Mat. Stud. 2012, 37 (1), 109-112.
-
Macdonald I.G. Symmetric Functions and Orthogonal Polynomials.
University Lecture Series, Vol. 12, AMS, Providence, RI, 1997.
-
Rosas M.H.
MacMahon symmetric functions, the partition lattice, and Young subgroups.
J. Combin. Theory Ser. A 2001, 96, 326-340.
doi: 10.1006/jcta.2001.3186
-
Zagorodnyuk A., Kravtsiv V.
Symmetric polynomials on the product of Banach spaces.
Carpathian Math. Publ. 2010, 2 (1), 59-71. (in Ukrainian)