The Journal of the Indian Mathematical Society

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On a Test for the Completeness (L2) of a Normal Orthogonal Set and its Applications


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1 Central College, Bangalore, India
     

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Steinhaus and Kaczmarz have given the following test on page 95 of their Theorie der orthogonal Reihen:-

A necessary and sufficient condition for the completeness (L2) of a normal orthogonal (O.N.) set {Φn} in (a, b) is that for a ≤ α ≤ β ≤ b.


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  • On a Test for the Completeness (L2) of a Normal Orthogonal Set and its Applications

Abstract Views: 198  |  PDF Views: 0

Authors

K. S. K. Iyengar
Central College, Bangalore, India

Abstract


Steinhaus and Kaczmarz have given the following test on page 95 of their Theorie der orthogonal Reihen:-

A necessary and sufficient condition for the completeness (L2) of a normal orthogonal (O.N.) set {Φn} in (a, b) is that for a ≤ α ≤ β ≤ b.