Mots-clés : Følner sequence.
@article{AA_2020_32_6_a4,
author = {N. Nikolski and A. Pushnitski},
title = {Szeg\H{o}-type limit theorems for {\textquotedblleft}multiplicative {Toeplitz{\textquotedblright}} operators and {non-F{\o}lner} approximations},
journal = {Algebra i analiz},
pages = {101--123},
year = {2020},
volume = {32},
number = {6},
language = {en},
url = {http://geodesic.mathdoc.fr/item/AA_2020_32_6_a4/}
}
N. Nikolski; A. Pushnitski. Szegő-type limit theorems for “multiplicative Toeplitz” operators and non-Følner approximations. Algebra i analiz, Tome 32 (2020) no. 6, pp. 101-123. http://geodesic.mathdoc.fr/item/AA_2020_32_6_a4/
[1] Ara P., Lledó F., Yakubovich D., “Følner sequences in operator theory and operator algebras”, Oper. Theory Adv. Appl., 242, Birkhäuser-Springer, Basel, 2014, 1–24 | MR | Zbl
[2] Balazard M., “Fonctions arithmétiques multiplicativement monotones”, Bull. Belg. Math. Soc. Simon Stevin, 26:2 (2019), 161–176 | DOI | MR | Zbl
[3] Bédos E., “On Følner nets, Szegő's theorem and other eigenvalue distribution theorems”, Expo. Math., 15:3 (1997), 193–228 | MR | Zbl
[4] Böttcher A., Silbermann B., Introduction to large truncated Toeplitz matrices, Universitext, Springer-Verlag, New York, 1999 | DOI | MR | Zbl
[5] Böttcher A., Otte P., “The first Szegő limit theorem for non-selfadjoint operators in the Følner algebra”, Math. Scand., 97:1 (2005), 115–126 | DOI | MR | Zbl
[6] Hagen R., Roch S., Silbermann B., $C^*$-algebras and numerical analysis, Marcel Dekker, 2001 | MR
[7] Hedenmalm H., Lindqvist P., Seip K., “A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$”, Duke Math. J., 86:1 (1997), 1–37 | DOI | MR | Zbl
[8] Hilberdink T., “Singular values of multiplicative Toeplitz matrices”, Linear Multilinear Algebra, 65:4 (2017), 813–829 | DOI | MR | Zbl
[9] Laptev A., Safarov Yu., “Szegő type limit theorems”, J. Funct. Anal., 138:2 (1996), 544–559 | DOI | MR | Zbl
[10] Levitan B. M., Pochti-periodicheskie funktsii, GITTL, 1953 | MR
[11] Li D., Queffélec H., Introduction to Banach spaces: analysis and probability, v. 2, Cambridge Stud. Adv. Math., 167, Cambridge Univ. Press, Cambridge, 2018 | MR | Zbl
[12] Nikolski N., Hardy spaces, Cambridge Stud. Adv. Math., 179, Cambridge Univ. Press, Cambridge, 2019 | MR | Zbl
[13] Nikolski N., Toeplitz matrices and operators, Cambridge Univ. Press, Cambridge (to appear) | Zbl
[14] Otte P., “An abstract Szegő theorem”, J. Math. Anal. Appl., 289:1 (2004), 167–179 | DOI | MR | Zbl
[15] Queffélec H., Queffélec M., Diophantine approximation and Dirichlet series, Harish-Chandra Res. Inst. Lecture Notes, 2, Hindustan Book Agency, New Delhi, 2013 | MR | Zbl
[16] Ramachandra K., On the mean-value and omega-theorems for the Riemann zeta-function, Lectures Math. Phys., 85, Tata Inst. Fundam. Res., Bombay, India, 1995 | MR | Zbl
[17] Simon B., Orthogonal polynomials on the unit circle, v. 1, Amer. Math. Soc. Colloquium Publ., 54, Classical theory, no. 1, Amer. Math. Soc., Providence, RI, 2005 | MR
[18] Szegő G., “Ein Grenzwertsatz über die Toeplitzschen Determinanten einer reellen positiven Funktion”, Math. Ann., 76:4 (1915), 490–503 | DOI | MR | Zbl
[19] Szegő G., “Beiträge zur Theorie der Toeplitzsche Formen. I”, Math. Z., 6:3–4 (1920), 167–202 | DOI | MR
[20] Titchmarsh E. C., The theory of the Riemann zeta-function, Second ed., Oxford Univ. Press, New York, 1986 | MR | Zbl
[21] Toeplitz O., “Zur Theorie der Dirichletschen Reihen”, Amer. J. Math., 60:4 (1938), 880–888 | DOI | MR
[22] Verblunsky S., “On positive harmonic functions”, Proc. London Math. Soc. (2), 40 (1935), 290–320 | MR