Displaying similar documents to “Functions of the form ∑ i = 1 N f i ( x ) g i ( t ) in L 2 ”

On some geometric properties of certain Köthe sequence spaces

Yunan Cui, Henryk Hudzik, Tao Zhang (1999)

Mathematica Bohemica

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It is proved that if a Kothe sequence space X is monotone complete and has the weakly convergent sequence coefficient WCS ( X ) > 1 , then X is order continuous. It is shown that a weakly sequentially complete Kothe sequence space X is compactly locally uniformly rotund if and only if the norm in X is equi-absolutely continuous. The dual of the product space ( ⨁ i = 1 ∞ X i ) Φ of a sequence of Banach spaces ( X i ) i = 1 ∞ , which is built by using an Orlicz function Φ satisfying the Δ 2 -condition, is computed isometrically (i.e....

Truncations of Gauss' square exponent theorem

Ji-Cai Liu, Shan-Shan Zhao (2022)

Czechoslovak Mathematical Journal

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We establish two truncations of Gauss’ square exponent theorem and a finite extension of Euler’s identity. For instance, we prove that for any positive integer n , ∑ k = 0 n ( - 1 ) k 2 n - k k ( q ; q 2 ) n - k q k + 1 2 = ∑ k = - n n ( - 1 ) k q k 2 , where n m = ∏ k = 1 m 1 - q n - k + 1 1 - q k and ( a ; q ) n = ∏ k = 0 n - 1 ( 1 - a q k ) .