Almost everywhere convergence of prolate spheroidal series
نویسندگان
چکیده
منابع مشابه
Almost Everywhere Convergence of Series in L
We answer positively a question of J. Rosenblatt (1988), proving the existence of a sequence (ci) with ∑∞ i=1 |ci| = ∞, such that for every dynamical system (X,Σ, m, T ) and f ∈ L1(X), ∑∞i=1 cif(T ix) converges almost everywhere. A similar result is obtained in the real variable context.
متن کاملMean and Almost Everywhere Convergence of Fourier-neumann Series
Let Jμ denote the Bessel function of order μ. The functions xJα+β+2n+1(x 1/2), n = 0, 1, 2, . . . , form an orthogonal system in L2((0,∞), xα+βdx) when α+ β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the Lp((0,∞), xαdx)-norm. Also, we describe the space in which the span of the system is dense and we show some of ...
متن کاملThe surprising almost everywhere convergence of Fourier-Neumann series
For most orthogonal systems and their corresponding Fourier series, the study of the almost everywhere convergence for functions in L requires very complicated research, harder than in the case of the mean convergence. For instance, for trigonometric series, the almost everywhere convergence for functions in L is the celebrated Carleson theorem, proved in 1966 (and extended to L by Hunt in 1967...
متن کاملChromatic Series and Prolate Spheroidal Wave Functions
The Ignjatovic theory of chromatic derivatives and series is extended to include other series. In particular series of prolate spheroidal wave functions are used to replace the orthogonal polynomial series in this theory. It is extended further to prolate spheroidal wavelet series that enables us to combine chromatic series with sampling series.
متن کاملOn hp-convergence of prolate spheroidal wave functions and a new well-conditioned prolate-collocation scheme
Article history: Received 11 October 2013 Received in revised form 27 January 2014 Accepted 6 March 2014 Available online 18 March 2014
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: Illinois Journal of Mathematics
سال: 2020
ISSN: 0019-2082
DOI: 10.1215/00192082-8622664