Abstract:
By the von Neumann inequality for homogeneous polynomials there exists a positive constant Ck,q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T1.... Tn) with ∑n i=1 Tiq ≤ 1 [EQUATION PRESENTED] we have For fixed k and q, we study the asymptotic growth of the smallest constant Ck,qn as n (the number of variables/operators) tends to infinity. For q = ∞, we obtain the correct asymptotic behavior of this constant (answering a question posed by Dixon in the 1970s). For 2 ≤ q < ∞ we improve some lower bounds given by Mantero and Tonge, and prove the asymptotic behavior up to a logarithmic factor. To achieve this we provide estimates of the norm of homogeneous unimodular Steiner polynomials, i.e. polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems. © 2018 De Gruyter.
Registro:
Documento: |
Artículo
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Título: | Asymptotic estimates on the von Neumann inequality for homogeneous polynomials |
Autor: | Galicer, D.; Muro, S.; Sevilla-Peris, P. |
Filiación: | Departamento de Matemática-PAB i, Facultad de Cs. Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Cmno Vera S/N, Valencia, 46022, Spain
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Año: | 2018
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Volumen: | 2018
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Número: | 743
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Página de inicio: | 213
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Página de fin: | 227
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DOI: |
http://dx.doi.org/10.1515/crelle-2015-0097 |
Título revista: | Journal fur die Reine und Angewandte Mathematik
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Título revista abreviado: | J. Reine Angew. Math.
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ISSN: | 00754102
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00754102_v2018_n743_p213_Galicer |
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Citas:
---------- APA ----------
Galicer, D., Muro, S. & Sevilla-Peris, P.
(2018)
. Asymptotic estimates on the von Neumann inequality for homogeneous polynomials. Journal fur die Reine und Angewandte Mathematik, 2018(743), 213-227.
http://dx.doi.org/10.1515/crelle-2015-0097---------- CHICAGO ----------
Galicer, D., Muro, S., Sevilla-Peris, P.
"Asymptotic estimates on the von Neumann inequality for homogeneous polynomials"
. Journal fur die Reine und Angewandte Mathematik 2018, no. 743
(2018) : 213-227.
http://dx.doi.org/10.1515/crelle-2015-0097---------- MLA ----------
Galicer, D., Muro, S., Sevilla-Peris, P.
"Asymptotic estimates on the von Neumann inequality for homogeneous polynomials"
. Journal fur die Reine und Angewandte Mathematik, vol. 2018, no. 743, 2018, pp. 213-227.
http://dx.doi.org/10.1515/crelle-2015-0097---------- VANCOUVER ----------
Galicer, D., Muro, S., Sevilla-Peris, P. Asymptotic estimates on the von Neumann inequality for homogeneous polynomials. J. Reine Angew. Math. 2018;2018(743):213-227.
http://dx.doi.org/10.1515/crelle-2015-0097