References
- Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebra of
symmetric holomorphic functions on \(\ell
_p\). Bull. Lond. Math. Soc. 2003, 35
(2003), 55–64.
- 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 (2), art. no. 41.
doi:10.3390/axioms11020041
- Chernega I., Galindo P., Zagorodnyuk A. Some algebras of
symmetric analytic functions and their spectra. Proc. Edinburgh
Math. Soc. 2012, 55 (2012), 125–142.
- Chernega I., Holubchak O., Novosad Z., Zagorodnyuk A. Continuity
and hypercyclicity of composition operators on algebras of symmetric
analytic functions on Banach spaces. European J. Math. 2020,
6 (2020), 153–163. doi:10.1007/s40879-019-00390-z
- 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
- 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 Fı́s. Nat. Ser. A Math. RACSAM 2020, 114.
doi:10.1007/s13398-020-00791-w
- Glaisher J.W.L. On the Product \(1^1.2^2.3^3\dots n^n\). Messenger
Math. 1878, 7, 43–47.
- Halushchak S.I. 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.
- Halushchak S.I. Isomorphisms of some algebras of analytic
functions of bounded type on Banach spaces. Mat. Stud. 2021,
56 (1), 106–112. doi:10.30970/ms.56.1.106-112
- Kravtsiv V., Vasylyshyn T., Zagorodnyuk A. On Algebraic Basis of
the Algebra of Symmetric Polynomials on \(l_p(\mathbb{C}^n)\). J. Funct. Spaces
2017, 2017 (7). doi:10.1155/2017/4947925
- Mujica J. Complex Analysis in Banach Spaces. Elsevier Sci. Publ.,
North Holland, 1986.
- Novosad Z., Zagorodnyuk A. Analytic Automorphisms and
Transitivity of Analytic Mappings. Mathematics 2020,
8 (12). doi:10.3390/math8122179
- Titchmarsh E.C. The Theory of Functions (2nd ed.). Oxford University
Press, London, 1939.
- Vasylyshyn T. Algebras of entire symmetric functions on spaces of
Lebesgue measurable essentially bounded functions. J. Math. Sci.
(N.Y.) 2020, 246 (2), 264–276.
doi:10.1007/s10958-020-04736-x
- Vasylyshyn T. Symmetric analytic functions on the Cartesian power
of the complex Banach space of Lebesgue measurable essentially bounded
functions on \([0,1]\). J. Math.
Anal. Appl. 2022, 509 (2).
doi:10.1016/j.jmaa.2021.125977
- 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
- Vasylyshyn T.V., Zahorodniuk V.A. Weakly symmetric functions on
spaces of Lebesgue integrable functions. Carpathian Math. Publ.
2022, 14 (2), 437–441.
doi:10.15330/cmp.14.2.437-441
- Zagorodnyuk A., Hihliuk A. Classes of Entire Analytic Functions
of Unbounded Type on Banach Spaces. Axioms 2020, 9
(4). doi:10.3390/axioms9040133
- Zagorodnyuk A., Hihliuk A. Entire Analytic Functions of Unbounded
Type on Banach Spaces and Their Lineability. Axioms 2021,
10 (3). doi:10.3390/axioms10030150