Pointwise universal trigonometric series
نویسندگان
چکیده
منابع مشابه
Pointwise Convergence of Trigonometric Series
We establish two results in the pointwise convergence problem of a trigonometric series [An] £ cne inl with lim Hm £ I bTck | = 0 |n|< -x. * Jn-»oo \k\-n for some nonnegative integer m. These results not only generalize Hardy's theorem, the Jordan test theorem and Fatou's theorem, but also complement the results on pointwise convergence of those Fourier series associated with known 1}-convergen...
متن کاملUniversal series by trigonometric system in weighted Lμ1 spaces
is said to be universal in X with respect to rearrangements, if for any f ∈ X the members of (1.1) can be rearranged so that the obtained series ∑∞ k=1 fσ(k) converges to f by norm of X . Definition 1.2. The series (1.1) is said to be universal (in X) in the usual sense, if for any f ∈ X there exists a growing sequence of natural numbers nk such that the sequence of partial sums with numbers nk...
متن کاملRearrangements of Trigonometric Series and Trigonometric Polynomials
Abstract. The paper is related to the following question of P. L. Ul’yanov: is it true that for any 2π-periodic continuous function f there is a uniformly convergent rearrangement of its trigonometric Fourier series? In particular, we give an affirmative answer if the absolute values of Fourier coefficients of f decrease. Also, we study a problem how to choose m terms of a trigonometric polynom...
متن کاملLacunary Trigonometric Series. Ii
where E c [0, 1] is any given set o f positive measure and {ak} any given sequence of real numbers. This theorem was first proved by R. Salem and A. Zygmund in case of a -0, where {flk} satisfies the so-called Hadamard's gap condition (cf. [4], (5.5), pp. 264-268). In that case they also remarked that under the hypothesis (1.2) the condition (1.3) is necessary for the validity of (1.5) (cf. [4]...
متن کاملOn Lacunary Trigonometric Series.
1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...
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: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.07.004