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PROPERTIES OF A CLASS OF INTEGRAL FUNCTIONS*

PROPERTIES OF A CLASS OF INTEGRAL FUNCTIONS* DEMONSTRA TIO MATHEMATICAVol. XIINo 11979S. K. Agarwal, S. K. BosePROPERTIES OF A CLASS OF INTEGRAL FUNCTIONS*1. IntroductionThe object of t h i s paper i s to study some algebraic andtopological properties of a c l a s s of integral functions [ l ](1)s1 =< f = f(z) =the principal value ofZ] an=oa1/2 n+1zn2n+1n=o< <*=>for a l l n has been taken.We prove that S^ forms a commutative Banach algebrawithout identity which i s separable and dense in i t s e l f asa topological space. Further we show that a subset, od S^ i sa complete vector l a t t i c e . Now S^, S^, . . . can be defined onthe same lines and i t can easily be seen that they a l l havesimilar properties as those of S^. Furthejr, they are a l li d e a l s of S^.Since the elements of S^ s a t i s f y the condition£n=oi t follows that1lim(a|n= limi a n / ^ C - ,1 2 n+1,2n+1 n(|a Q= lim)a.2 n+1* We are thankful to the referee for his suggestions.- 63 -A c l a s s of i http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

PROPERTIES OF A CLASS OF INTEGRAL FUNCTIONS*

Agarwal, S. K.; Bose, S. K.
Demonstratio Mathematica , Volume 12 (1): 8 – Jan 1, 1979
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References (1)

Publisher
de Gruyter
Copyright
© by S. K. Agarwal
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1979-0105
Publisher site
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Abstract

DEMONSTRA TIO MATHEMATICAVol. XIINo 11979S. K. Agarwal, S. K. BosePROPERTIES OF A CLASS OF INTEGRAL FUNCTIONS*1. IntroductionThe object of t h i s paper i s to study some algebraic andtopological properties of a c l a s s of integral functions [ l ](1)s1 =< f = f(z) =the principal value ofZ] an=oa1/2 n+1zn2n+1n=o< <*=>for a l l n has been taken.We prove that S^ forms a commutative Banach algebrawithout identity which i s separable and dense in i t s e l f asa topological space. Further we show that a subset, od S^ i sa complete vector l a t t i c e . Now S^, S^, . . . can be defined onthe same lines and i t can easily be seen that they a l l havesimilar properties as those of S^. Furthejr, they are a l li d e a l s of S^.Since the elements of S^ s a t i s f y the condition£n=oi t follows that1lim(a|n= limi a n / ^ C - ,1 2 n+1,2n+1 n(|a Q= lim)a.2 n+1* We are thankful to the referee for his suggestions.- 63 -A c l a s s of i

Journal

Demonstratio Mathematica – de Gruyter

Published: Jan 1, 1979

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