On Nörlund summation and ergodic theory, with applications to power series of Hilbert contractions

• Autorzy: Cuny C. , Weber M.

Identyfikatory

DOI

10.4064/ba8121-12-2017

• Języki publikacji: EN

Abstrakty

EN

We show that if a = (a_n)_n∈N is a good weight for the dominated weighted ergodic theorem in L^p, p > 1, then the Nörlund matrix N_a = {a_i−j / A_i}_0≤j≤i, A_i = ∑ⁱ_k=0|a_k|, is bounded on ℓ^p(N). We study the regularity (convergence in norm and almost everywhere) of operators in ergodic theory: power series of Hilbert contractions and power series ∑_n∈N a_n P_n f of L²-contractions, and establish similar close relations to the Nörlund operator associated to the modulus coefficient sequence (|a_n|)_n∈N.

Słowa kluczowe

EN

Nörlund matrix; weighted ergodic theorem; power series of contractions

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2018
• Tom: Vol. 66, no. 1
• Strony: 69--85
• Opis fizyczny: Bibliogr. 30 poz.

Twórcy

autor

Cuny C.

• Institut de Sciences Exactes et Appliquées, Université de la Nouvelle Calédonie, B.P. 4477, F-98847 Noumea Cedex

autor

Weber M.

• IRMA, 10 rue du Général Zimmer, 67084 Strasbourg Cedex, France

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).