Refinement of some necessary conditions

• Autorzy: Leindler L.
• Języki publikacji: EN

Abstrakty

EN

The traditional monotonicity requirement on the coefficients of orthogonal series is weakened to almost, or locally almost monotonicity assumptions in connection with the necessary conditions of convergence and absolute Cesaro summability of Haar series. Similar generalization is established regarding Fourier series and general orthogonal series.

Słowa kluczowe

EN

orthogonal series; Haar system; summability methods; locally almost decreasing sequences

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2004
• Tom: Vol. 44, nr spec.
• Strony: 145--154
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Leindler L.

• Bolyai Institute, University of Szeged ARADI VÉRTANUK TERE 1, H-6720 Szeged, Hungary

Bibliografia

• [1] G. Alexits, Konvergenzprobleme der Orthogonalreihen, Budapest, 1960.
• [2] L. Csernyák and L. Leindler, Über die Divergenz der Partialsummen von Orthogonalreihen, Acta Sci. Math. (Szeged) 27 (1966), 55-61.
• [3] L. Leindler, Über Konvergenz- und Summationseigenschaften von Haarschen Reihen, Acta Sci. Math. (Szeged) 26 (1965), 19-30.
• [4] L. Leindler, Über Strukturbedingungen für Fourierreihen, Math. Zeitschr. 88 (1965), 418-431.
• [5] L. Leindler, Über die verallgemeinerte de la Vallée- Poussinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Hungar. 16 (1965), 375-387.
• [6] L. Leindler, On the newly generalized absolute Cesaro summability of orthogonal series, Acta Math. Hungar. 68 (1975), 295-316.
• [7] L. Leindler, On the divergence of partial sums of orthogonal series, Publ. Math. (Debrecen) 64 (2004).

Uwagi

Dedicated to Professor Julian Musielak on his 75th birthday.