References

  1. Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebra of symmetric holomorphic functions on $\ell _p$. Bull. London Math. Soc. 2003, 35 (1), 55-64. doi: 10.1112/S0024609302001431
  2. Chernega I.V. Symmetric polynomials and holomorphic functions on infinite dimensional spaces. Journal of Vasyl Stefanyk Precarpathian National University 2015, 2 (4), 23-49. doi: 10.15330/jpnu.2.4.23-49
  3. Chernega I., Galindo P., Zagorodnyuk A. Some algebras of symmetric analytic functions and their spectra. Proc. Edinb. Math. Soc. (2) 2012, 55 (1), 125-142. doi: 10.1017/S0013091509001655
  4. 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
  5. Dieudonne J.A., Carrell J.B. Invariant Theory, old and new. In: Advances in Mathematics, 4 (1). Elsevier, 1970. 1-80. doi: 10.1016/0001-8708(70)90015-0
  6. Kravtsiv V. Algebra of block-symmetric polynomials: generating elements and the transletion operator. Math. Bull. Shevchenko Sci. Soc. 2011, 8, 107-121. (in Ukrainian)
  7. 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.
  8. Macdonald I.G. Symmetrc Functions and Orthogonal Polynomials. In: University lecture series, 12. Providence, R.I., 1997.
  9. Nemirovskii A.S., Semenov S.M. On polynomial approximation of functions on Hilbert space. Mat. USSR-Sbornik 1973, 21 (2), 255-277. doi: 10.1070/SM1973v021n02ABEH002016 (translation of Mat. Sb. (N.S.) 1973, 92 (2), 257-281. (in Russian))
  10. Papush D.E. On the growth of entire functions with “planar” zeros. J. Soviet Math. 1990, 49 (2), 930-935. doi: 10.1007/BF02205642 (translation of Teoriya Funkt., Funkts. Analiz i Ikh Priloz. 1987, 47, 117-125. (in Russian))
  11. Weyl H. The classical group: their invariants and representations. Princeton university press, Princenton, New Jersey, 1973.
  12. Zagorodnyuk A.V., Kravtsiv V.V. Spectra of algebra of block-symmetrical analitical functions. Applied Problem of Mech. and Math. 2011, 9, 47-54. (in Ukrainian)
  13. Zagorodnyuk A.V., Kravtsiv V.V. Symmetric polynomials on the product of Banach spaces. Carpathian Math. Publ. 2010, 2 (1), 59-71. (in Ukrainian)