- Autor
- TitelOn the uniform theory of lacunary series
- Datei
- Persistent Identifier
- Erschienen inNumber Theory – Diophantine Problems, Uniform Distribution and Applications
- LicenceCC BY
- ISBN978-3-319-55357-3
- Download Statistik816
- Peer ReviewNein
- AbstractThe theory of lacunary series starts with Weierstrass’ famous example (1872) of a continuous, nondifferentiable function and now we have a wide and nearly complete theory of lacunary subsequences of classical orthogonal systems, as well as asymptotic results of thin subsequences of general function systems. However, many applications of lacunary series in harmonic analysis, orthogonal function theory, Banach space theory, etc. require uniform limit theorems for such series, i.e. theorems holding simultaneously for a class of lacunary series, and such results are much harder to prove than dealing with individual series. The purpose of this paper is to give a survey of uniformity theory of lacunary series and discuss new results in the field. In particular, we study the permutation-invariance of lacunary series and their connection with Diophantine equations, uniform limit theorems in Banach space theory, resonance phenomena for lacunary series and lacunary series with random gaps.