التفاصيل البيبلوغرافية
العنوان: |
Comparison of speeds of convergence in Riesz-type families of summability methods. |
المؤلفون: |
Šeletski, Anna1, Tali, Anne1 atali@tlu.ee |
المصدر: |
Proceedings of the Estonian Academy of Sciences. 2008, Vol. 57 Issue 2, p70-80. 11p. |
مصطلحات موضوعية: |
*RIESZ spaces, *MATHEMATICAL sequences, *SUMMABILITY theory, *ABEL integral equations, *RINGS of integers |
Abstract (English): |
We deal with Riesz-type families (see Proc. Estonian Acad. Sci. Phys. Math., 2002, 51, 18-34 and Acta Sci. Math. (Szeged), 2004, 70, 639-657) of summability methods Aα for converging functions and sequences. The methods Aα in a Riesztype family depend on a continuous parameter α; and are connected through certain generalized integral Nörlund methods. By extending and applying the results of Stadtmüller and Tali (Anal. Math., 2003, 29, 227-242), we compare speeds of convergence in a Riesz-type family. As expected, the speed of convergence cannot increase if we switch from one summability method to a stronger one. Comparative estimations for speeds are found. In particular, the families of integral Riesz methods, generalized integral Nörlund methods, and Abel-and Borel-type summability methods are considered. Numerical examples are given. [ABSTRACT FROM AUTHOR] |
Abstract (Estonian): |
On võrreldud funktsioonide (ja jadade) summeeruvust eri summeerimismenetluste korral Rieszi tüüpi peredes (vt [6] ja [8]). On üldistatud ja rakendatud töös [7] saadud tulemusi jadade summeeruvuskiiruste võrdlemisel. On tõestatud teoreem, mis võimaldab võrrelda summeeruvuskiirusi eri menetluste korral Rieszi-tüüpi peres. On hinnatud summeeruvuskiirusi võrratuste abil. Näidetena on vaadeldud Rieszi ja üldistatud Nörlundi integraalmenetlusi, samuti Abelining Boreli-tüüpi summeerimismenetlusi. [ABSTRACT FROM AUTHOR] |
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