Analysis, algebra, and computers in mathematical research: by Mats Gyllenberg, Lars-Erik Persson PDF

By Mats Gyllenberg, Lars-Erik Persson

ISBN-10: 0585328285

ISBN-13: 9780585328287

ISBN-10: 0824792173

ISBN-13: 9780824792176

Offering the court cases of the twenty-first Nordic Congress of Mathematicians at Luleå college of expertise, Sweden, this striking reference discusses fresh advances in research, algebra, stochastic methods, and using desktops in mathematical learn.

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Extra info for Analysis, algebra, and computers in mathematical research: proceedings of the Twenty-first Nordic Congress of Mathematicians

Example text

1 , ????2 ), lim ???? 1 ????−1 ∑ ????(???????? (????1 ))????(???????? (????2 )) = 0. ???? ????=0 The link between product-null functions, spectral measure and the Kronecker fac­ tor is outlined in the following lemma of Rudolph. Note that this lemma actually cor­ rects the corresponding statement in the BFKO proof. 22. For ???? ∈ ????∞ (????) with ∫ ???????????? = 0, the following are equivalent: 34 | Idris Assani and Kimberly Presser (1) (2) (3) (4) ???? is product-null. The spectral measure of ???? is nonatomic. e. ???? ∈ K⊥ . e. ergodic component ????̂ of ???? × ???? ∫ ????(????1 )????(????2 )????????̂ = 0.

Unfortunately, there was an error in the proof of Wiener and Wintner. However, the theorem is true and has been proven multiple times using a wide variety of techniques. The first correct version of the proof was given by H. Furstenberg [50] using the notions of joinings and generic points. We will see later the role of joinings and generic points in the proof of the Return Times Theorem. Another proof of the Wiener–Wintner Theorem which uses Van der Corput’s inequality [60] was given by Bourgain [27] in 1990.

1 , ????2 ), lim ???? 1 ????−1 ∑ ????(???????? (????1 ))????(???????? (????2 )) = 0. ???? ????=0 The link between product-null functions, spectral measure and the Kronecker fac­ tor is outlined in the following lemma of Rudolph. Note that this lemma actually cor­ rects the corresponding statement in the BFKO proof. 22. For ???? ∈ ????∞ (????) with ∫ ???????????? = 0, the following are equivalent: 34 | Idris Assani and Kimberly Presser (1) (2) (3) (4) ???? is product-null. The spectral measure of ???? is nonatomic. e. ???? ∈ K⊥ . e. ergodic component ????̂ of ???? × ???? ∫ ????(????1 )????(????2 )????????̂ = 0.

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Analysis, algebra, and computers in mathematical research: proceedings of the Twenty-first Nordic Congress of Mathematicians by Mats Gyllenberg, Lars-Erik Persson


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