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.M., Cole B.J., Gamelin T.W.
Spectra of algebras of analytic functions on a Banach space.
J. Reine Angew. Math. 1991, 415, 51-93.
doi: 10.1515/crll.1991.415.51
-
Aron R.M., Cole B.J., Gamelin T.W.
Weak-star continuous analytic funtions.
Canad. J. Math. 1995, 47 (4), 673-683.
doi: 10.4153/CJM-1995-035-1
-
Aron R.M., Falcó J., García D., Maestre M.
Algebras of symmetric holomorphic functions of several complex variables.
Rev. Mat. Complut. 2018, 31, 651-672.
doi: 10.1007/s13163-018-0261-x
-
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.V.
A semiring in the spectrum of the algebra of symmetric analytic functions in the space $\ell_1.$
J. Math. Sci. 2016, 212, 38-45.
doi: 10.1007/s10958-015-2647-3
(translation of Mat. Metody Fiz.-Mekh. Polya 2014, 57, 35-40. (in Ukrainian))
-
Chernega I., Holubchak O., Novosad Z., Zagorodnyuk A.
Continuity and hypercyclicity of composition operators on algebras of symmetric analytic functions on Banach spaces.
Eur. J. Math. 2020, 6, 153-163.
doi: 10.1007/s40879-019-00390-z
-
Chernega I., Galindo P., Zagorodnyuk A.
Some algebras of symmetric analytic functions and their spectra.
Proc. Edinb. Math. Soc. (2) 2011, 55 (1), 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., Galindo P., Zagorodnyuk A.
A multiplicative convolution on the spectra of algebras of symmetric analytic functions.
Rev. Mat. Complut. 2014, 27 (2), 575-585.
doi: 10.1007/s13163-013-0128-0
-
Dineen S.
Complex analysis on infinite-dimensional spaces.
Springer-Verlag, London, 1999.
-
Falcó J., García D., Jung M., Maestre M.
Group invariant separating polynomials on a Banach space.
Publ. Mat. To appear.
-
Galindo P., Vasylyshyn T., Zagorodnyuk A.
Analytic structure on the spectrum of the algebra of symmetric analytic functions on $L_\infty$.
Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM
2020, 114 (56).
doi: 10.1007/s13398-020-00791-w
-
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, 1712-1726.
doi: 10.1002/mana.201700314
-
Galindo P., Vasylyshyn T., Zagorodnyuk A.
The algebra of symmetric analytic functions on $L_\infty$.
Proc. Roy. Soc. Edinburgh Sect. A
2017 147 (4), 743-761.
doi: 10.1017/S0308210516000287
-
García D., Maestre V., Zalduendo I.
The spectra of algebras of group-symmetric functions.
Proc. Edinb. Math. Soc. (2) 2019, 62 (3), 609-623.
doi: 10.1017/S0013091518000603
-
Gonzaléz M., Gonzalo R., Jaramillo J.
Symmetric polynomials on rearrangement invariant function spaces.
J. Lond. Math. Soc. (2) 1999, 59, 681-697.
doi: 10.1112/S0024610799007164
-
Jawad F., Karpenko H., Zagorodnyuk A.,
Algebras generated by special symmetric polynomials on $\ell_1$.
Carpathian Math. Publ. 2019, 11 (2), 335-344.
doi: 10.15330/cmp.11.2.335-344
-
Jawad F., Zagorodnyuk A.
Supersymmetric Polynomials on the Space of Absolutely Convergent Series.
Symmetry 2019, 11 (9), 1111.
doi: 10.3390/sym11091111
-
Kravtsiv V.
Analogues of the newton formulas for the block-symmetric polynomials on $\ell_p(\mathbb{C}^s)$.
Carpathian Math. Publ. 2020, 12 (1), 17-22.
doi: 10.15330/cmp.12.1.17-22
-
Symmetric Functions and Orthogonal Polynomials.
University Lecture Series, 12, AMS, Providence, RI, 1997.
-
Mujica J.
Ideals of holomorphic functions on Tsirelson's space.
Arch. Math. (Basel) 2001, 76, 292-298.
doi: 10.1007/s000130050571
-
Zagorodnyuk A.
Spectra of Algebras of Entire Functions on Banach Spaces.
Proc. Amer. Math. Soc. 2006, 134, 2559-2569.
doi: 10.1090/S0002-9939-06-08260-8