Decrease of Fourier coefficients of stationary measures
نویسندگان
چکیده
منابع مشابه
Transformations of Fourier Coefficients
Introduction. In 1923 M. Fekete [2]2 introduced the concept of factor sequences that left invariant the class of a Fourier series. That is, Fekete investigated the conditions to which a sequence of constants (X„) must be subjected in order that (X„a„, X„i„) be Fourier coefficients of a function of the same class, K, as that of the function determined by (an, bn). Whenever (X„) has this property...
متن کاملFourier Transforms of Stationary Processes
We consider the asymptotic behavior of Fourier transforms of stationary and ergodic sequences. Under sufficiently mild conditions, central limit theorems are established for almost all frequencies as well as for a given frequency. Applications to the widely used linear processes and iterated random functions are discussed. Our results shed new light on the foundation of spectral analysis in tha...
متن کاملThe Calculation of Fourier Coefficients
The Möbius inversion technique is applied to the Poisson summation formula. This results in expressions for the remainder term in the Fourier coefficient asymptotic expansion as an infinite series. Each element of this series is a remainder term in the corresponding Euler-Maclaurin summation formula, and the series has specified convergence properties. These expressions may be used as the basis...
متن کاملFourier Coefficients of Hecke Eigenforms
We provide systematic evaluations, in terms of binary quadratic representations of 4p, for the p-th Fourier coefficients of each member f of an infinite class C of CM eigenforms. As an application, previously conjectured evaluations of three algebro-geometric character sums can now be formulated explicitly without reference to eigenforms. There are several non-CM newforms that appear to share s...
متن کاملFourier Coefficients of Modular Forms
These notes describe some conjectures and results related to the distribution of Fourier coefficients of modular forms. This is a rough draft and these notes should forever be considered incomplete.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 2018
ISSN: 0025-5831,1432-1807
DOI: 10.1007/s00208-018-1743-3