References

  1. Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebra of symmetric holomorphic functions on \(\ell _p\). Bull. Lond. Math. Soc. 2003, 35 (1), 55–64. doi:10.1112/S0024609302001431
  2. Aron R.M., Falcó J., García D., Maestre M. Algebras of symmetric holomorphic functions of several complex variables. Rev. Mat. Complut. 2018, 31 (3), 651–672. doi:10.1007/s13163-018-0261-x
  3. 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
  4. Aron R., Galíndo 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
  5. 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
  6. Chernega I., Galindo P., Zagorodnyuk A. Some algebras of symmetric analytic functions and their spectra. Proc. Edinb. Math. Soc. 2012, 55 (1), 125–142. doi:10.1017/S0013091509001655
  7. 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. 2020, 114, 56. doi:10.1007/s13398-020-00791-w
  8. Gonzaléz M., Gonzalo R., Jaramillo J. Symmetric polynomials on rearrangement invariant function spaces. J. London Math. Soc. 1999, 59 (2), 681–697. doi:10.1112/S0024610799007164
  9. Jawad F., Zagorodnyuk A. Supersymmetric polynomials on the space of absolutely convergent series. Symmetry 2019, 11 (9), 1111. doi:10.3390/sym11091111
  10. Lindestrauss J., Tzafriri L. Classical Banach Spaces I: Sequence Spaces. In: Ergebnisse der mathematik und ihrer Grenzgebiete, 92. Springer-Verlag, Berlin, Heidelberg, New York, 1977.
  11. Macdonald I.G. Symmetric Functions and Orthogonal Polynomials. In: University Lecture Series, 12. AMS, Providence, R.I., 1998.
  12. Martsinkiv M., Zagorodnyuk A. Approximations of symmetric functions on Banach spaces with symmetric bases. Symmetry 2021, 13 (12), 2318. https://doi.org/10.3390/sym13122318
  13. Mujica J. Complex Analysis in Banach Spaces. Elsevier, Amsterdam, 1986.
  14. Nemirovskii A.S., Semenov S.M. On polynomial approximation of functions on Hilbert space. Math. USSR Sb. 1973, 21 (2), 255–277. (translation of Math. Sb. 1973, 92(134) (2(10)), 257–281. (in Russian))
  15. Speyer D.E., Sturmfels B. Tropical mathematics. Math. Mag. 2009, 82 (3), 163–173. doi:10.1080/0025570X.2009.11953615
  16. Vasylyshyn T. Symmetric functions on spaces \(\ell_p(\mathbb{R}^n)\) and \(\ell_p(\mathbb{C}^n).\) Carpathian Math. Publ. 2020, 12 (1), 5–16. doi:10.15330/cmp.12.1.5-16
  17. Vasylyshyn T.V., Zagorodnyuk A.V. Symmetric polynomials on the Cartesian power of the real Banach space \(L_\infty[0,1]\). Mat. Stud. 2020, 53 (2), 192–205. doi:10.30970/ms.53.2.192-205
  18. Vasylyshyn T., Zagorodnyuk A. Continuous symmetric 3-homogeneous polynomials on spaces of Lebesgue measurable essentially bounded functions. Methods Funct. Anal. Topology 2018, 24 (4), 381–398.
  19. Weaver N. Lipschitz Algebras. World Scientific, New Jersey, 1999.