The Journal of the Indian Mathematical Society

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Some Uniqueness Theorems for Functions of Class Lp


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1 Madras University, India
     

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Let {Φn(x)}, n=1, 2, . . . , be a sequence of measurable functions of a real variable x defined almost everywhere in an interval a≤x≤b. Let f(x) be a function belonging to the Lebesgue class Lp(p>0) and let {Φn} be such that all the integrals

cn(f)=∫f(x)Φn(x)dx                                                 (1)

exist as L-integrals.


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  • Some Uniqueness Theorems for Functions of Class Lp

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Authors

V. Ganapathy Iyer
Madras University, India

Abstract


Let {Φn(x)}, n=1, 2, . . . , be a sequence of measurable functions of a real variable x defined almost everywhere in an interval a≤x≤b. Let f(x) be a function belonging to the Lebesgue class Lp(p>0) and let {Φn} be such that all the integrals

cn(f)=∫f(x)Φn(x)dx                                                 (1)

exist as L-integrals.