Multivariable Bohr inequalities

• Autores: Gelu Popescu
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 11, 2007, págs. 5283-5317
• Idioma: inglés
• DOI: 10.1090/s0002-9947-07-04170-0
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• Resumen

  • Operator-valued multivariable Bohr type inequalities are obtained for:

    (i) a class of noncommutative holomorphic functions on the open unit ball of , generalizing the analytic functions on the open unit disc;

    (ii) the noncommutative disc algebra and the noncommutative analytic Toeplitz algebra ;

    (iii) a class of noncommutative selfadjoint harmonic functions on the open unit ball of , generalizing the real-valued harmonic functions on the open unit disc;

    (iv) the Cuntz-Toeplitz algebra , the reduced (resp. full) group -algebra (resp. ) of the free group with generators;

    (v) a class of analytic functions on the open unit ball of .

    The classical Bohr inequality is shown to be a consequence of Fejér's inequality for the coefficients of positive trigonometric polynomials and Haager- up-de la Harpe inequality for nilpotent operators. Moreover, we provide an inequality which, for analytic polynomials on the open unit disc, is sharper than Bohr's inequality.