Rodney Nillsen - Böcker
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2 produkter
2 produkter
849 kr
Skickas inom 7-10 vardagar
Randomness and Recurrence in Dynamical Systems aims to bridge a gap between undergraduate teaching and the research level in mathematical analysis. It makes ideas on averaging, randomness, and recurrence, which traditionally require measure theory, accessible at the undergraduate and lower graduate level. The author develops new techniques of proof and adapts known proofs to make the material accessible to students with only a background in elementary real analysis. Over 60 figures are used to explain proofs, provide alternative viewpoints and elaborate on the main text. The book explains further developments in terms of measure theory. The results are presented in the context of dynamical systems, and the quantitative results are related to the underlying qualitative phenomena - chaos, randomness, recurrence and order. The final part of the book introduces and motivates measure theory and the notion of a measurable set, and describes the relationship of Birkhoff's Individual Ergodic Theorem to the preceding ideas. Developments in other dynamical systems are indicated, in particular L vy's result on the frequency of occurence of a given digit in the partial fractions expansion of a number.
Del 1586 - Lecture Notes in Mathematics
Difference Spaces and Invariant Linear Forms
Häftad, Engelska, 1994
271 kr
Skickas inom 10-15 vardagar
Difference spaces arise by taking sums of finite or fractional differences. Linear forms which vanish identically on such a space are invariant in a corresponding sense. The difference spaces of L2 (Rn) are Hilbert spaces whose functions are characterized by the behaviour of their Fourier transforms near, for example the origin. The aim of this text is to establish connections between these spaces and differential operators, singular integral operators and wavelets. It discusses aspects of these ideas which emphasize invariant linear forms on locally compact groups. The work primarily presents new results, but does so from a unified viewpoint, which emphasises connections with related work.