Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T04:06:32.622Z Has data issue: false hasContentIssue false

On finite sections of the multiplicative Hilbert inequalities

Published online by Cambridge University Press:  08 April 2021

Charif Abdallah Benyamine*
Affiliation:
University of Bordeaux, CNRS, Bordeaux INP, IMB, UMR 5251, F-33405Talence, France

Abstract

We determine the asymptotic behavior of the eigenvalues of finite sections of the multiplicative Hilbert matrices.

Type
Article
Copyright
© Canadian Mathematical Society 2021

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beurling, A., The collected works of Arne Beurling . In: Carleson, L., Malliavin, P., Neuberger, J., and Wermer, J. (eds), Complex analysis, Contemporary Mathematicians, 1. Birkhäuser Boston, Inc., Boston, MA, 1989.Google Scholar
Bolmarcich, J., The behavior of the maximum value of finite sections of a class of bilinear forms . J. Math. Anal. Appl. 56(1976), no. 1, 84101.CrossRefGoogle Scholar
Brevig, O. F., Perfekt, K. M., Seip, K., Siskakis, A. G., and Vukotić, D., The multiplicative Hilbert matrix . Adv. Math. 302(2016), 410432.CrossRefGoogle Scholar
de Bruijn, N. G. and Wilf, H. S., On Hilbert’s inequality in $n$ dimensions . Bull. Amer. Math. Soc. 68(1962), 7073.CrossRefGoogle Scholar
Hardy, G. H., Littlewood, J. E., and Pólya, G., Inequalities. Cambridge University Press, Cambridge, 1934.Google Scholar
Miheisi, N. and Pushnitski, A., A Helson matrix with explicit eigenvalue asymptotics . J. Funct. Anal. 275(2018), no. 4, 967987.CrossRefGoogle Scholar
Perfekt, K. M. and Pushnitski, A., On Helson matrices: moment problems, non-negativity, boundedness, and finite rank . Proc. Lond. Math. Soc. (3) 116(2018), no. 1, 101134.CrossRefGoogle Scholar
Perfekt, K. M. and Pushnitski, A., On the spectrum of the multiplicative Hilbert matrix . Ark. Mat. 56(2018), no. 1, 163183.CrossRefGoogle Scholar
Shields, A., An analogue of the Fejér-Riesz theorem for the Dirichlet space. In: Conference on harmonic analysis in honor of Antoni Zygmund, (Chicago, Ill., 1981), Wadsworth Mathematics Series, I, II, Wadsworth, Belmont, CA, 1983, pp. 810820.Google Scholar
Widom, H., On the eigenvalues of certain hermitian operators . Trans. Amer. Math. Soc. 88(1958), 491522.CrossRefGoogle Scholar
Wilf, H. S., Finite sections of some classical inequalities . Springer, Heidelberg, 1970.10.1007/978-3-642-86712-5CrossRefGoogle Scholar