References

  1. Aron R., Galindo P., Pinasco D., Zalduendo I. Group-symmetric holomorphic functions on a Banach space. Bull. Lond. Math. Soc. 2016, 48, 779–796. doi:10.1112/blms/bdw043
  2. Bandura A., Kravtsiv V., Vasylyshyn T. Algebraic Basis of the Algebra of All Symmetric Continuous Polynomials on the Cartesian Product of \(\ell_p\)-Spaces. Axioms 2022, 11, 41. doi:10.3390/axioms11020041
  3. Baziv N., Zagorodnyuk A. Analytic Invariants of Semidirect Products of Symmetric Groups on Banach Spaces. Symmetry 2023, 15, 2117. doi:10.3390/sym15122117
  4. Chernega I., Dmytryshyn R., Novosad Z., Sharyn S., Zagorodnyuk A. Symmetric Analytic Functions on Banach Spaces Associated with the Cantor Set. Symmetry 2026, 18 (5), 716. doi:10.3390/sym18050716
  5. Chernega I., Galindo P., Zagorodnyuk A. On the spectrum of the algebra of bounded-type symmetric analytic functions on \(l_1.\) Math. Nachr. 2024, 297, 3835–3846. doi:10.1002/mana.202300415
  6. Chernega I., Martsinkiv M., Vasylyshyn T., Zagorodnyuk A. Applications of supersymmetric polynomials in statistical quantum physics. Quantum Rep. 2023, 5, 683–697. doi:10.3390/quantum5040043
  7. Dineen S. Complex Analysis on Infinite Dimensional Spaces. Springer: Berlin/Heidelberg, Germany, 1999. doi:10.1007/978-1-4471-0869-6
  8. Faryma D., Kimak V., Kravtsiv V., Zagorodnyuk A. On block-supersymmetric polynomials on Banach spaces. Algebra Discrete Math. 2025, 40 (1), 14–26. doi:10.12958/adm2416
  9. González M., Gonzalo R., Jaramillo J.A. Symmetric polynomials on rearrangement-invariant function spaces. J. Lond. Math. Soc. 1999, 59, 681–697. doi:10.1112/S0024610799007164
  10. Hryniv R., Kravtsiv V., Vasylyshyn T., Zagorodnyuk A. Symmetric and supersymmetric polynomials on \(\ell_p\) and partition functions in quantum statistical physics. Physica Scripta 2025, 100, 075208. doi:10.1088/1402-4896/adde1e
  11. Kravtsiv V. Block-supersymmetric polynomials on spaces of absolutely convergent series. Symmetry 2024, 16, 179. doi.org:10.3390/sym16020179
  12. Reed M., Simon B. Methods of Modern Mathematical Physics. Vol. 1 Functional Analysis. Academic Press, San Diego, California, 1980.
  13. Schmidt H.J., Schnack J. Partition functions and symmetric polynomials. Am. J. Phys. 2002, 70, 53–57. doi:10.1119/1.1412643.
  14. Schmidt H.J., Schnack J. Symmetric polynomials in physics. In: Gazeau J.-P., Kerner R., Antoine J.-P., Metens S., Thibon J.-Y. (Eds.) IOP: Bristol, Philadelphia, 2003, 173, 147–152.
  15. Vasylyshyn T.V. Algebras of symmetric and block-symmetric functions on spaces of Lebesgue measurable functions. Carpathian Math. Publ. 2024, 16, 174–189. doi:10.15330/cmp.16.1.174-189