Approximation of functions and their conjugates in Lp and uniform metric by Euler means

• Autorzy: Volosivets S. S. , Tyuleneva A. A.

Identyfikatory

DOI

10.1515/dema-2018-0013

• Języki publikacji: EN

Abstrakty

EN

For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.

Słowa kluczowe

EN

Euler means; functions of bounded p-variation; best approximation; conjugate function; degree of approximation; Lp; sharpness

PL

metoda Eulera; funkcja o ograniczonej zmienności; najlepsza aproksymacja; funkcja sprzężona; rząd aproksymacji; Lp; ostrość

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 141--150
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Volosivets S. S.

• Saratov State University, Faculty of Mechanics and Mathematics, 410012, Saratov, Astrakhanskaya St., 83, Russian Federation

autor

Tyuleneva A. A.

• Saratov State University, Faculty of Mechanics and Mathematics, 410012, Saratov, Astrakhanskaya St., 83, Russian Federation

Bibliografia

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Uwagi

PL

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