Application of generalized Rademacher
functions to investigation of algebras of symmetric analytic
functions on $L_p[0,1]$

I. V. Chernega; A. V. Zagorodnyuk

Actions of symmetric polynomials on generalized Rademacher functions are investigated. Some applications to algebras of symmetric analytic functions on the unit ball of $L_p[0,1]$, $1\leq p<\infty,$ are described.

1. Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebra of symmetric holomorphic functions on $\ell _p$, Bull. Lond. Math. Soc. 35 (2003), 55-64.

2. Aron R.M., Lacruz M., Ryan R.A., Tonge A.M. The generalized Rademacher Functions, Note Math., 12 (1992), 15–25.

3. Aron R.M., Cole B.J., Gamelin T.W. Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math. 415 (1991), 51–93.

4. Aron R.M., Cole B.J., Gamelin T.W. Weak-star continuous analytic funtions, Can. J. Math. 47 (1995), 673–683.

5. Aron R.M., Galindo P., Garcia D., Maestre M. Regularity and algebras of analytic function in infinite dimensions, Trans. Amer. Math. Soc. 348 (1996), 543–559.

6. Aron R.M., Globevnik J. Analytic functions on $c_{0}$, Revista Matem\'atica (Madrid), 2 (1989), 27-34.

7. Diestel J., Jarchow H., Tonge A. Absolutely summing operators, vol. 43, Cambridge University Press, Cambridge, 1995.

8. Gonzalez M., Gonzalo R., Jaramillo J. Symmetric polynomials on rearrangement invariant function spaces, J. London Math. Soc. 59 (1999), 681–697.

9. Gonzalo R., Jaramillo J. Smoothness and estimates of sequences in Banach spaces, Israel J. Math. 89 (1995), 321–341.

10. Nemirovskii A.S., Semenov S.M. On polynomial approximation of functions on Hilbert space, Mat. USSR Sbornik 21 (1973), 255–277.

11. Пузирьова I. Симетричнi аналiтичнi функцi∙ в $L_p,$ Мат.\ методи i фiз.-мех.\ поля 45 (2002), № 1, 56--60.

12. Загороднюк А. В., Про максимальнi iдеали алгебри цiлих функцiй на банаховому просторi, Мат. методи i фiз.-мех. поля 43 (2000), № 3, 16–23.

	Application of generalized Rademacher functions to investigation of algebras of symmetric analytic functions on $L_p[0,1]$
Author	I. V. Chernega, A. V. Zagorodnyuk Institute of Applied Problems of Mechanics and Mathematics
Abstract	Actions of symmetric polynomials on generalized Rademacher functions are investigated. Some applications to algebras of symmetric analytic functions on the unit ball of $L_p[0,1]$, $1\leq p<\infty,$ are described.
Keywords	symmetric polynomial, generalized Rademacher function, unit ball
DOI	doi:10.30970/ms.21.1.64-70
Reference	1. Alencar R., Aron R., Galindo P., Zagorodnyuk A. Algebra of symmetric holomorphic functions on $\ell _p$, Bull. Lond. Math. Soc. 35 (2003), 55-64. 2. Aron R.M., Lacruz M., Ryan R.A., Tonge A.M. The generalized Rademacher Functions, Note Math., 12 (1992), 15–25. 3. Aron R.M., Cole B.J., Gamelin T.W. Spectra of algebras of analytic functions on a Banach space, J. Reine Angew. Math. 415 (1991), 51–93. 4. Aron R.M., Cole B.J., Gamelin T.W. Weak-star continuous analytic funtions, Can. J. Math. 47 (1995), 673–683. 5. Aron R.M., Galindo P., Garcia D., Maestre M. Regularity and algebras of analytic function in infinite dimensions, Trans. Amer. Math. Soc. 348 (1996), 543–559. 6. Aron R.M., Globevnik J. Analytic functions on $c_{0}$, Revista Matem\'atica (Madrid), 2 (1989), 27-34. 7. Diestel J., Jarchow H., Tonge A. Absolutely summing operators, vol. 43, Cambridge University Press, Cambridge, 1995. 8. Gonzalez M., Gonzalo R., Jaramillo J. Symmetric polynomials on rearrangement invariant function spaces, J. London Math. Soc. 59 (1999), 681–697. 9. Gonzalo R., Jaramillo J. Smoothness and estimates of sequences in Banach spaces, Israel J. Math. 89 (1995), 321–341. 10. Nemirovskii A.S., Semenov S.M. On polynomial approximation of functions on Hilbert space, Mat. USSR Sbornik 21 (1973), 255–277. 11. Пузирьова I. Симетричнi аналiтичнi функцi∙ в $L_p,$ Мат.\ методи i фiз.-мех.\ поля 45 (2002), № 1, 56--60. 12. Загороднюк А. В., Про максимальнi iдеали алгебри цiлих функцiй на банаховому просторi, Мат. методи i фiз.-мех. поля 43 (2000), № 3, 16–23.
Pages	64-70
Volume	21
Issue	1
Year	2004
Journal	Matematychni Studii
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Application of generalized Rademacher functions to investigation of algebras of symmetric analytic functions on $L_p[0,1]$