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Abstract:

We consider different kinds of convergence of homogeneous polynomials and multilinear forms in random variables. We show that for a variety of complex random variables, the almost sure convergence of the polynomial is equivalent to that of the multilinear form, and to the square summability of the coefficients. Also, we present polynomial Khintchine inequalities for complex gaussian and Steinhaus variables. All these results have no analogues in the real case. Moreover, we study the Lp-convergence of random polynomials and derive certain decoupling inequalities without the usual tetrahedral hypothesis. We also consider convergence on "full subspaces" in the sense of Sjögren, both for real and complex random variables, and relate it to domination properties of the polynomial or the multilinear form, establishing a link with the theory of homogeneous polynomials on Banach spaces. © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:On the convergence of random polynomials and multilinear forms
Autor:Carando, D.; Dimant, V.; Pinasco, D.
Filiación:Departamento de Matemática, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria (C1428EGA), Buenos Aires, Argentina
CONICET, Argentina
Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284 (B1644BID), Victoria, Buenos Aires, Argentina
Departamento de Matemáticas y Estadística, Universidad T. Di Tella, Miñones 2177 (C1428ATG), Buenos Aires, Argentina
Palabras clave:Multilinear forms in random variables; Polynomial Khintchine inequalities; Polynomials in random variables
Año:2011
Volumen:261
Número:8
Página de inicio:2135
Página de fin:2163
DOI: http://dx.doi.org/10.1016/j.jfa.2011.06.004
Título revista:Journal of Functional Analysis
Título revista abreviado:J. Funct. Anal.
ISSN:00221236
CODEN:JFUAA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00221236_v261_n8_p2135_Carando

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Citas:

---------- APA ----------
Carando, D., Dimant, V. & Pinasco, D. (2011) . On the convergence of random polynomials and multilinear forms. Journal of Functional Analysis, 261(8), 2135-2163.
http://dx.doi.org/10.1016/j.jfa.2011.06.004
---------- CHICAGO ----------
Carando, D., Dimant, V., Pinasco, D. "On the convergence of random polynomials and multilinear forms" . Journal of Functional Analysis 261, no. 8 (2011) : 2135-2163.
http://dx.doi.org/10.1016/j.jfa.2011.06.004
---------- MLA ----------
Carando, D., Dimant, V., Pinasco, D. "On the convergence of random polynomials and multilinear forms" . Journal of Functional Analysis, vol. 261, no. 8, 2011, pp. 2135-2163.
http://dx.doi.org/10.1016/j.jfa.2011.06.004
---------- VANCOUVER ----------
Carando, D., Dimant, V., Pinasco, D. On the convergence of random polynomials and multilinear forms. J. Funct. Anal. 2011;261(8):2135-2163.
http://dx.doi.org/10.1016/j.jfa.2011.06.004