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Abstract:

Let P:Cn→C be an m-homogeneous polynomial given by P(x)=∑1≤j1≤…≤jm≤ncj1…jmxj1…xjm. Defant and Schlüters defined a non-symmetric associated m-form LP:(Cn)m→C by LP(x(1),…,x(m))=∑1≤j1≤…≤jm≤ncj1…jmxj1 (1)…xjm (m). They estimated the norm of LP on (Cn,‖⋅‖)m by the norm of P on (Cn,‖⋅‖) times a (clog⁡n)m2 factor for every 1-unconditional norm ‖⋅‖ on Cn. A symmetrization procedure based on a card-shuffling algorithm which (together with Defant and Schlüters’ argument) brings the constant term down to (cmlog⁡n)m−1 is provided. Regarding the lower bound, it is shown that the optimal constant is bigger than (clog⁡n)m/2 when n≫m. Finally, the case of ℓp-norms ‖⋅‖p with 1≤p<2 is addressed. © 2018 Elsevier Inc.

Registro:

Documento: Artículo
Título:Some remarks on non-symmetric polarization
Autor:Marceca, F.
Filiación:Departamento de Matemática - Pab I, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina
IMAS, CONICET, Argentina
Palabras clave:Card-shuffling; Main triangle projection; Multilinear forms; Polarization; Polynomials
Año:2018
Volumen:466
Número:2
Página de inicio:1486
Página de fin:1498
DOI: http://dx.doi.org/10.1016/j.jmaa.2018.06.067
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v466_n2_p1486_Marceca

Referencias:

  • Bennett, G., Unconditional convergence and almost everywhere convergence (1976) Z. Wahrsch. Verw. Gebiete, 34 (2), pp. 135-155
  • Defant, A., Schlüters, S., Non-symmetric polarization (2017) J. Math. Anal. Appl., 445 (2), pp. 1291-1299
  • Dineen, S., Complex Analysis on Infinite Dimensional Spaces (1999), Springer-Verlag London; Fisher, R., Yates, F., Statistical Tables for Biological, Agricultural and Medical Research (1938), p. 285. , Oliver and Boyd Edinburgh; Kwapień, S., Pełczyński, A., The main triangle projection in matrix spaces and its applications (1970) Studia Math., 34 (1), pp. 43-67
  • Kwapień, S., Woyczyński, W., Random Series and Stochastic Integrals: Single and Multiple (1992), Birkhauser Basel; McConnell, T., Taqqu, M., Decoupling of Banach-valued multilinear forms in independent symmetric Banach-valued random variables (1987) Probab. Theory Related Fields, 75 (4), pp. 499-507
  • Pełczyński, A., Commensurate sequences of characters (1988) Proc. Amer. Math. Soc., 104 (2), pp. 525-531

Citas:

---------- APA ----------
(2018) . Some remarks on non-symmetric polarization. Journal of Mathematical Analysis and Applications, 466(2), 1486-1498.
http://dx.doi.org/10.1016/j.jmaa.2018.06.067
---------- CHICAGO ----------
Marceca, F. "Some remarks on non-symmetric polarization" . Journal of Mathematical Analysis and Applications 466, no. 2 (2018) : 1486-1498.
http://dx.doi.org/10.1016/j.jmaa.2018.06.067
---------- MLA ----------
Marceca, F. "Some remarks on non-symmetric polarization" . Journal of Mathematical Analysis and Applications, vol. 466, no. 2, 2018, pp. 1486-1498.
http://dx.doi.org/10.1016/j.jmaa.2018.06.067
---------- VANCOUVER ----------
Marceca, F. Some remarks on non-symmetric polarization. J. Math. Anal. Appl. 2018;466(2):1486-1498.
http://dx.doi.org/10.1016/j.jmaa.2018.06.067